HER face and voice have become familiar, and not just because they are beautiful, but the public know almost nothing about Bonnie Greer. Invariably announced as a playwright and critic - in that order - whenever she appears on television or radio, far more people have seen her on the BBC's Newsnight Review programme than have ever attended a performance of Jitterbug, Munda Negra, Dancing On Blackwater, or any other drama she has written for the British stage in the 20 years since she moved here from America. And while Greer is frequently invited to comment on cultural matters in the UK, she is rarely asked anything personal.

"Yeah, " she says, "but that's a good thing. When I heard that you guys wanted some kind of in-depth interview, I thought, 'Ohhhh . . . shit'. It's not that I have anything to hide, it's just that there's a lot of information out there people don't really need. In the future, I think the grail will be for nobody to know anything about you."

There is, though, certain information that she thinks people do need, and her work as a dramatist is expressly designed to supply it. Greer's latest play, Ella, Meet Marilyn, will make its debut run this month at the Edinburgh Festival Fringe. This afternoon, Greer lets me watch a rehearsal at the Rosemary Branch Pub And Theatre in north London, along with her English husband, David Hutchins, and various other interested parties. We sit down to watch Marilyn Monroe, as portrayed by former Coronation Street star Sally Lindsay, make her own deceptively naive case against racial prejudice.

"People say that black people must be inferior because they don't make great art, " reasons Lindsay on the stage, speaking in a decent approximation of that breathy baby voice familiar from Monroe's movies, and putting Bonnie Greer's words in the mouth of the icon. "But Shakespeare is Duke Ellington. Bach is Charlie Parker. It's the same beauty, the same complexity, just in a different form." Jazz legend Ella Fitzgerald is played here by Rain Pryor - the daughter of comic genius Richard Pryor - looking on in wary agreement before venturing the opinion that Monroe was "ahead of her time, and she didn't even know it".

That particular line came from the singer herself, who said it long after Monroe had cheerfully ignored the rules of mid-1950s American segregation by pressuring the owner of Hollywood's glamorous whitesonly Mocambo nightclub to let Fitzgerald play five nights in a row. Few people are now familiar with this strange-but-true showbiz story - reason enough for Greer to write a play about it.

"I wrote this basically because the information has been suppressed, " she says when the show is over, leaning into my ear from the row behind. "And if you don't control the information, it controls you. That's certainly true in the case of Marilyn Monroe, who was a victim of information control even after her death. She was the biggest movie star in the world and she made this kind of stand for Ella Fitzgerald. People at the time didn't understand it, so they glossed over it, and now not many even know about it. Which means that it has never really been celebrated."

Having first heard about this encounter on the Biography Channel, Greer has imagined it as a fleeting alignment of the stars, a moment stolen in the backstage area of history, and it's unexpectedly moving to hear Monroe tell Fitzgerald, with the exposed heart of a true fan, that she wakes up and goes to sleep listening to her records. Today, the author gives all credit to the cast and crew, standing up to tell them, by way of praise: "Anyone who knows me knows I'm never lost for words . . . " Afterwards, she says she feels like smoking a cigar, but she and her husband offer to buy me lunch in the pub instead. Greer's kindness often shows in her work as a critic, and makes co-panellists on Newsnight Review seem narcissistic and meanspirited by comparison. "That's because they think being a critic means that you criticise. It's not the same thing. Those words are not related in the way some

people assume. It's not really about whether something is good or bad, whether you like it or don't. I see my job as just to do the homework and talk about it."

It would be possible to make guesses at Greer's character on the basis of opinions she has given in the media. Her favourite piece of prose is The Fire Next Time, James Baldwin's despondent and crystalline essay on race. She thinks identity should be considered fluid, rather than fixed, and that includes her own. She doesn't have much time for the self-obsession displayed by fellow members of the baby boom generation, who are "frightened of time and of life", even as they rule the world.

She is a feminist, but won't necessarily agree that today's young women are a problem. "I've got friends who think Jordan and Paris Hilton are awful, " says Greer, "but they forget when we were that age and had hair down to our asses. We made much more of a radical departure from our parents, caused much more calamity. I don't know what these young women are all about, but I trust them to find their own means of expression."

These are just opinions, and Greer doesn't seem to find them as interesting as other people do. "What I think is what I think. The fact that I'm always being asked shows how small this country is, and how lazy this culture can be. Some people have a lot to say but never get asked. Other people are on speed dial, and I seem to be one of them."

AT58, she looks better for her age than anyone I've ever met, and cooler, for lack of a better word, than she appears on television. She was born, in Chicago, the same year as "cool" itself. "Cool, " says Greer, "was the buzzword for 1948, when the whole jazz thing changed. Swing bands died out and be-bop came in. So then you got Charlie Parker, and Miles [Davis], and all these guys who were suddenly 'cool'."

Prince Charles was also born that year, which apparently prompted American anglophiles (including Bogart and Bacall) to name their own babies Bonnie. Greer's father was a Mississippi sharecropper - "about the lowest category of farmer that you could be" - who had spent time in England as a serviceman during the second world war.

"His experience shaped me before I even came into the world, in that the war made clear to him what the United States was about." Black troops were not allowed to carry weapons until so many white soldiers had been lost that commanders had no choice but to arm them, by which time her father had reached the same conclusion that James Baldwin described in The Fire Next Time. "You must put yourself, " wrote Baldwin, "in the skin of a man who is wearing the uniform of his country, is a candidate for death in its defence, and who is called a 'nigger' by his comrades-in-arms . . . who at the same time, as a human being, is far freer in a strange land than he has ever been at home."

This, says Greer, is how her father felt about England, "where he met black RAF men who were treated like human beings in his own context", and the reason why he later understood his daughter's decision to move there. "There is oppression here too, of course, but not with a capital 'O'."

After the war, he worked in a cannery six nights a week for 40 years. The oldest of seven children, Greer grew up "frankly, in the ghetto", and received a Catholic education at the best school her parents could afford. James Baldwin had renounced Christianity when he could no longer reconcile it with his skin colour, his intellect, or his sense of morality, but Greer's own youthful realisation that almost all the saints were white never quite put her off the church (she later played Joan Of Arc on stage in Paris, and has since made several documentaries about her search for black faces in Western art and religious iconography).

"I was a cradle Catholic, " she says. "The priest who baptised me is still a part of our family. I think everything I write is probably about my Catholicism, in a strange sort of way. It's in my DNA." She concedes that this may have more to do with deep-seated gratitude than true faith. Greer isn't sure if she believes in God, and thinks this life is all there is, "but at the same time I believe my father is in heaven, because he wanted to go there, and deserved to".

Theatre, she says, has always been a part of her too. She started writing plays when she was nine and only stopped in the late 1960s because events made the arts seem "frivolous". "The civil rights movement, the women's movement, the poverty movement, the anti-war movement - all that stuff was real. In those days I wanted to be a lawyer, to be a function of what I called truth. A lot of my generation of black students felt that was the best way to carry on the struggle. You either became a lawyer or a Black Panther - those choices were almost interchangeable as a means to redress. I even worked with the Black Panthers.

"But then I did a law course, and the professor walked in and said right away that he didn't believe in women practising law. I thought, 'Do I want to spend four years in this kind of company?' And the answer was, 'No, I don't.'" She went on to study drama in Chicago, under legendarily hard-nosed local playwright David Mamet, and worked at New York's Actor's Studio with the great stage and screen director Elia Kazan. "I was taught that theatre is supposed to slow the world down so it can be looked at, and the person who looks is not supposed to be the same when they walk out. Otherwise, there's no f***ing point. Art is not a leisure activity. It's about engagement."

The UK has given Greer "my husband, and my second life . . . my life in the arts". Which is to say, she loves the place - racism is rare and tacit enough not to interfere with her happiness, and she doesn't mind if Britain's ambivalent attitude to America is sometimes reflected in the way people treat her. "I don't think it's helpful for Americans to carry around the myth that they are loved by the UK. It's rubbish. It's what my next play is about."

Greer first came here, 20 years ago this summer to act in a play at the Edinburgh Festival, and stayed because it seemed to offer what she was looking for. "Back then, " she says, "the English theatre I saw was multi-ethnic to its deepest core. I saw black theatre emerging from a black base, from companies who were engaged with the world. Maybe Thatcher was the catalyst." If so, perhaps Tony Blair is the reason why she now finds English theatre - as opposed to Irish or Scottish - "careerist and conservative".

"Young people don't seem to have an aesthetic, let alone a sense of engagement. They talk about writing as a career rather than something they're fired up about, and that sounds horrible to me."

All Greer can do is try to help. She's on the board of the British Museum (by appointment of the Prime Minister, whom she has never met, and hopes she never will, "because I was raised not to be rude to people") as well as the Serpentine Gallery and the London Film School, and serves as artistic director of the Talawa Theatre Company. Each of those posts requires a certain capacity for nurturing. The respect that she feels for her elders - Greer has made a conscious effort to keep her Chicago accent because she is determined to sound like her parents - she also extends to the young.

"I'm glad you said nurturing. I feel the same responsibility to those who are coming up behind me as I do to those who came before."

If you wanted to criticise Greer herself, with the kind of negativity she thinks the world doesn't need, you might consider her apparent inconsistencies. She describes her generation as "selfish" while admitting that she made a conscious decision not to have children for the sake of her own freedom. She says her ethos is "basically, fight the power" but also that her only ambition is "to kick back and have a really good time". If you have any respect for her opinion though, you'll consider that Greer's sense of identity is exactly as fluid as she wants it to be.

"The problem with being black is that your identity is assumed from the get-go. Actually, no, the problem is when you accept it. That's what makes you unhappy. And the only thing that matters is living life as you feel you're meant to. People get serious about books and plays, me included, but you should never forget it's all play. And in the end, it's all dust."

Ella, Meet Marilyn, opens at the Pleasance Dome tonight, and runs until August 28. Ticketline: 0131 226 0000 www. edfringe. com