Fiona Bradley, Florence Ingleby and Susanna Beaumont are bemused as our photographer clicks away. What, they ask, do they have in common? Why are they being interviewed together? The three curators know each other, of course, as they all run galleries in Edinburgh. Bradley’s is the Fruitmarket Gallery, the much praised public contemporary art space; Ingleby, with her husband Richard, runs the capital’s Ingleby Gallery, a leading private art space; Beaumont runs Doggerfisher, a small but beautifully formed gallery with an enviable stable of young artists which includes Lucy Skaer, who is in the running for this year’s Turner Prize.

What else do these three have in common? All are in their early-to-mid 40s. All three of them, today, are wearing wedge shoes. All are graceful and attractive. All three have moved to Edinburgh from elsewhere. Two work in the private sector, and one in the publicly funded realm. Oh, and they are all presenting new shows at next month’s Edinburgh Art Festival.

All three women are all exceptionally good at their jobs, and each, in their own way, has helped transform, by innovation, application, and imagination, the contemporary art scene in Edinburgh particularly and in Scotland more generally. Together, they have presented, nurtured and sold the cream of Scottish art in recent years – work by names such as Callum Innes, Alison Watt, Lucy Skaer, Claire Barclay, Louise Hopkins and Charles Avery, among many others.

Edinburgh, Beaumont points out as we stand high over its familiar landscape, is an easy city in which to escape, or at least it seems that way. There is little sense of urban claustrophobia, wherever you are standing. You can see hills, or the sea, or both, at every turn. For all three curators, it was an easy city to move to and to prosper.

Bradley, 43, grew up in Germany, where her father was in the forces, and spent her early years in Paderborn and Moenchengladbach. After school in Oxford, she studied art history at Cambridge, and then for an MA and a PhD at the Courtauld Institute in London. She then worked at the Tate in London and in Liverpool, before taking over at the Fruitmarket Gallery six years ago. “When I was at the Tate, I realised something was really going on in Scotland,” she says. The “defining moment,” was when Glasgow artist and filmmaker Douglas Gordon won the Turner Prize in 1996. “That really surprised some people,” she remembers. “You could sense this feeling of ‘who is this wild man from Scotland coming down to steal our prize?’”

“When I arrived, the Fruitmarket already had a certain profile,” she says, “but I wanted to build on that and give it a bit of ‘oomph’. I really wanted to show that Scottish artists can work on an international level and are international artists in themselves. Before, there was a tentativeness about showing Scottish artists alongside international ones.”

Florence Ingleby looks slightly embarrassed. “I would just like to add that I am here under false pretences,” she says. “I have not done any of this on my own.” Which, of course, is true. The Ingleby Gallery has always been run by both Ingleby, a native of Kent, and her husband Richard, from Helensburgh. For many years it was a close domestic arrangement: the gallery was in the couple’s house, at Carlton Terrace in Edinburgh. Ingleby, 43, married Richard in 1994 and the pair now have three daughters. Their gallery came into being after Ingleby quit her job as publicity director for Bloomsbury Publishing and Richard left his post at the Fine Arts Society in London. They decided to set up a gallery in Edinburgh which would show artists of international standing.

So far, it has worked beyond their most fevered imaginings. Earlier this year, the gallery moved from the couple’s home to large new premises behind the capital’s Waverley Station. She recalls: “Richard and I were in London, thinking, ‘what are we doing here?’ We had experienced working incredibly hard for other people. When I look back, it was a completely ridiculous decision to set up a gallery in our house, but we just thought, ‘sod it, we’ll give it a go, and if it doesn’t work, it doesn’t work’.”

But why choose private art dealing? “We didn’t want to be told what to do,” says Ingleby. “We didn’t want to be compromised by having backers or funders, or to be publicly accountable. We knew that it would be hugely threatening at times and quite scary, but the flipside of that was our freedom. From the very first moment, we were staggered that the gallery worked. There wasn’t anything else like us in Edinburgh, so the gallery very quickly made its mark, in a small-scale way.”

A successful show by Edinburgh College Of Art graduate and abstract painter Callum Innes in 2001 was one high point; an exhibition by the celebrated painter Alison Watt OBE in 2002 was another. The Ingleby Gallery, Ingleby says, knew it had found its niche. “There weren’t any private galleries at that stage showing contemporary work by artists of international stature, or for Scottish artists who wanted to show on the international stage,” she says. The couple’s risky move this year to a massive new gallery was necessary, she says. “Ultimately, it became difficult to show work in our house. We lived here and showed here and it was really bizarre that it worked. A lot of the artists would come and stay, and visitors would come and go. It’s bizarre that we did it for so long, but you got used to your life being extremely public.”

Beaumont, of Doggerfisher, is trying to explain how she came to be running one of the most exciting private galleries in Scotland, if not in the UK. Originally from Hereford, she studied art history in Manchester. In 1991, she upped sticks and lived in Cairo for four “extraordinary, amazing, intense” years. On returning to the UK, she came to live in Edinburgh. Beaumont had no plan, and didn’t know anyone in the city. She began by selling ice cream at the Assembly Rooms during the Fringe Festival, before becoming a respected arts critic at The List magazine. In 2000, she opened her own art gallery in a former garage in Edinburgh’s Gayfield Square.

Setting up her gallery in the early days, she says, was like “running down hill and not being able to stop”. That was eight frantic, but highly successful, years ago. Beaumont runs Doggerfisher on a small scale and describes it as a “lean and modest operation”. But, when she was in Cairo all those years ago, why did she think of relocating to Edinburgh? “It just seduced me,” she says. “But there’s a sense of laziness and complacency about a capital. Compared to Glasgow, Edinburgh is much more financially buoyant, or was before this year, and was resting on its good-looking laurels. I’ve always described Edinburgh as the best-looking person in the room. If you arrive at a party and there is a gorgeous person, and then you go and speak to them, they are sometimes a little boring. That ­friction exists with Edinburgh.”

Beaumont and Bradley have a particular connection this year in Lucy Skaer. The Cambridge-born conceptual artist is represented by Beaumont’s gallery Doggerfisher, and her “mid-career retrospective” exhibition at the Fruitmarket last year was part of the résumé which led to her nomination for the Turner Prize in April. Beaumont smiles. “It seemed to me that there were so many brilliant artists in Scotland, but there wasn’t a specific infrastructure to support them. Berlin, London, New York and Madrid all have contemporary, confident galleries and I felt Edinburgh should have one too. I was seeing all these artists and thought: ‘Damn it Edinburgh, you should have one too.’”

Bradley says she felt the same absence in Edinburgh. “No-one was consistently showing new work or publishing their work in books, which is a key thing for me,” she says. “I think publishing is a very important way of saying ‘here is my show’. Nothing gives me more pleasure than looking at the bookshelf space in my office which shows all the ­exhibitions we have done.”

Bradley, with the Fruitmarket, works in the public sector, which is a different sphere to Beaumont. “I am interested in how the art reacts with an audience,” she says. “There is also an element of idealism to it, yes. I would like to have tried the commercial world, but struggle with art being treated as a commodity.”

Ingleby has a different view. She feels the private sector also has a vital role for artists – selling their work and generating their income. “We are now reaching a point where a thriving private sector is vital to the arts scene in Scotland,” she says. “It’s very hard to be an artist in Scotland. There are no incentives to stay. There is no tax or rates relief, there’s no way to feel valued or appreciated, and that goes side by side with the lack of galleries. Glasgow has got it right as far as commercial galleries are concerned. I mean we [the Ingleby Gallery] are old farts now. It needs to be addressed.”

Beaumont is frustrated by Edinburgh’s attitude to its own environment. She is infuriated on the day we meet by the lacklustre public flowerbeds on the city’s Calton Hill. But, she adds, “I think Edinburgh has changed. I think we have managed to tickle the big institutions, the National Galleries, into buying contemporary art.

“But I am passionate about what Scotland, as a whole, can do. Most of my artists live in Glasgow, and we couldn’t be here if ­Glasgow wasn’t there – let’s be honest about that. The Edinburgh scene has sharpened over the years, but I feel the city needs to be ‘out there’ a little bit more.”

At least now there is an annual platform for contemporary art in Edinburgh, in the shape of the Edinburgh Art Festival, which is now in its sixth year. Bradley, Beaumont and Ingleby have all curated new shows for this year’s Festival. New work from Beck’s Futures prize-winner Rosalind Nashashibi will be displayed at Doggerfisher, Callum Innes returns to the Ingleby Gallery, and the Fruitmarket has an exhibition of the work of the late German-born American sculptor, Eva Hesse. “There is nothing to beat the feeling of working late on a new exhibition, knowing that something is new and unseen and wondering whether it’s going to be liked and looked at, and what the public will think of it,” says Bradley.

Beaumont agrees. “I’m just excited by good artists, and it doesn’t matter to me whether they are from Scotland or from elsewhere, but they have to be curious, pushing their practice, making work that is beautiful and moving, that is contemporary and not timid.”

Ingleby is also upbeat, although she admits the global financial crash, just after she opened her new gallery, was “absolutely terrifying”. “I do feel very confident of the work we show and the way we do it, and very proud of it, and I think that it will, because of the gallery’s scale now, have more of an impact. It’s important, right now, to not panic,” she says, smiling.

In closing, I ask the three women how they feel, with their disparate and varying lives and stories, being lumped together for one interview? Bradley is first to answer. “How do we feel? I would say that it’s important that women are running artistic institutions.” And then, to laughter from all those present, she adds: “It hasn’t escaped my notice, that there are no women running the National Galleries of Scotland.” She looks at the others before continuing. “That has certainly not escaped

our notice.”

Nashashibi/Skaer is at Doggerfisher August 1-September 26; Callum Innes is at Ingleby Gallery, August 5-September 19; Eva Hesse Studiowork is at The Fruitmarket Gallery August 5-October 25.