When Molly Taylor performed Love Letters To The Public Transport System just over a year ago as part of the National Theatre of Scotland's Reveal season, it was advertised as a work in progress.

While such a safety net covered everybody's back in case things went wrong, what audiences got was a lovingly crafted, semi-autobiographical monologue performed simply and beautifully by Taylor. It was the most fully rounded production of the Reveal season.

Taylor's real-life quest to track down the drivers of buses and trains who led the Liverpool-born performer to significant moments in her life – and indeed to significant others – returns for dates in schools and some public shows prior to a full Edinburgh Festival Fringe run as part of this year's Made in Scotland programme. Any fears that such a bespoke success story has been transformed into an all-singing, all-dancing spectacular are mercifully unfounded.

"It feels like Love Letters is about to take off on its own little adventure," Taylor explains, "and I'm really keen to get it out there.

"A year-and-a-half after this little show began, I've taken a kind of running leap at it and am getting a proper run at it, which is dead exciting, but pretty nerve-racking as well. I've actually only performed it six times, and it's been dormant since then, so I haven't reworked it in any way, and, to be honest, I don't know how much it's going to change or not. I knew from last time that it didn't need puppets, pyrotechnics or anything like that, but I'm in a place now where I want to renew it, but I don't want to overdo it either."

Director Graham Maley, who had worked at Liverpool's Unity Theatre as well as on monologues by Ronan O'Donnell and with the late Susannah York on the Shakespeare's Women series, has been drafted on to the production as an outside eye in what is a deeply instinctive show.

"Because Love Letters is so personal," Taylor says, "I've never really approached it as a text. I've just wanted to get the words in the right place. There's always a danger with something that you have done with absolutely no expectations, that the spirit of the piece is lost somehow. I know Love Letters has to have a bit of a polish, but I don't want to polish it so much that it loses that spirit. It's good to know that storytelling like this still has a role in theatre. It's great that you can do things on a grand scale, but there's still a place for little people like me."

Love Letters To The Public Transport System was born out of a crucial period in the life of a woman who, even after the acclaim the work received, sees herself as neither an actor nor a writer.

"The piece came out of a very happy period in my life," Taylor explains, "which followed a fairly low period, when I was being trampled on by a relationship. I was jobless and there was just nothingness. Then my life changed dramatically, just by making a couple of journeys from Liverpool to London.

"I got thinking that it would make a great speech for a wedding day to talk about how, if it wasn't for these train drivers getting people to places on time, some things in my life would never have happened. I'd sort of had this lovely year-long love affair with public transport and I just wanted to thank them."

With no wedding upcoming, this germ of an idea turned into the basis of the show. A former theatre studies student at Glasgow University, Taylor had joined the National Theatre of Scotland's associate programme, so had connection enough to approach NTS artistic development producer Caroline Newall, who gave her the resources for six months of research. The result of the umpteen meetings that followed was a series of real-life love stories that criss-crossed Taylor's own experiences, as a railway track might build up a network.

"For me it felt like a really energising and incredibly urgent thing to do," Taylor says of the experience. "The totally exciting thing about it was that I didn't know what it was going to be until just before the end. I wrote large sections of it on trains, because I don't have a car, and the whole thing was born out of love, really. I was stupidly in love with this person, and, instead of a faith or a belief system, I put faith into that. But you do have to be careful when you're doing something so personal because it treads a very fine line that can easily slip into indulgence."

The response to Love Letters, however, has left Taylor bowled over.

"I got loads of lovely letters," she says. "I even got a letter from the traffic commissioner of Scotland, who said it was her job to make buses safe for people. There's so many more stories you can find, and I don't know if I've got one of those faces, but people talk to me all the time about the most intimate details of their lives. I know I'm not a dramatist, and I think telling stories about my life isn't as creative as what playwrights do, so I keep things simple."

As with so many performers, Taylor discovered drama as a way of coping with her shyness. As a child, Taylor's sister – three years younger – became "a guaranteed audience of one.

"Whenever she played, I would turn that into a piece of character-based drama. I can't remember what the turning point was, but I must've put myself up for a play at school, and that changed everything. Drama was instructive, but it wasn't trying, it was just doing."

Taylor likens this epiphany to taking drugs for the first time. "You realise why people do it," she says, "because it's so much fun."

Taylor's school didn't do A-level drama, but her teacher, having spotted her potential, embarked on a course of individual tuition, during which "we spent a year talking about Brecht".

In Glasgow, Taylor's relationship with the NTS began on their production of The Wolves in the Walls, and has continued since Love Letters as one of the recipients of the Bank of Scotland Emerge programme for developing theatre-makers. Taylor also performed at Oran Mor in a piece by Gary McNair in which she ran on a treadmill throughout the entire show.

To describe Taylor as irrepressibly chirpy is both an understatement and a potential Scouse cliché. In a free-wheeling, if somewhat breathlessly one-sided conversation, her enthusiasm is irresistibly infectious.

I can't resist pointing out that she has just given me the benefit of her time for longer than her show lasts,

"I should've charged you a tenner," she says, laughing. "Everyone's a storyteller in Liverpool. It's the same in the west coast of Scotland. We just like to chat."

Love Letters To The Public Transport System, Dornie Hall, June 26; Macphail Centre, Ullapool, June 28; Macrobert Arts Centre, Stirling, July 5; Assembly Rooms, Edinburgh, August 2-26. www.nationaltheatrescotland.com.