Of course I have to ask Jill Bryson about the time she spent a night at the Brit Awards in the company of Prince.

This would have been back in 1985, the year Prince turned up at the Savoy Hotel to collect a Best International Artist award accompanied by a giant white bodyguard who looked a bit like Giant Haystacks' older brother.

You remember, don't you? Jill certainly does. She was there that night with her Strawberry Switchblade band mate and fellow Weegie Rose McDowall and they were seated at the same table as the now late and much lamented Purple One.

Did he say anything to you, Jill? "No," she screams. "You're joking. Absolutely not. He was on the other side of this big round table with his bodyguards. And they were crawling around on the floor. I don't know if they thought there was a suspicious package or something.

"I think he kept his dark glasses on as well. And he was so tiny. We just sat giggling on the other side of the table.

"It was great fun. I remember Neil Tennant was there and at that point I'm not sure if he was a Pet Shop Boy. He was still writing for Smash Hits. And I remember running about with him in the Savoy going into the kitchens and being ridiculous.

"But yes, Prince in his dark glasses and his bodyguards. It was surreal."

That was then. This is now. And right now Bryson, 53, is sitting in her living room in the home in Islington – "not the fashionable bit though," she points out – that she shares with her partner Martin and their 24-year-old daughter Jessie, assorted cats and, today, a mountain of thread and fabric.

The rest of today will be spent sewing costumes for her upcoming performance piece at the Glasgow School of Art at the end of the month; a recreation of an installation she mounted at the art school way back in 1981. She's doing it to help launch a new book Inventors of Tradition II, a new book exploring Scottish creativity organised by Atelier E.B. (aka artist Lucy McKenzie and designer Beca Lipscombe) and curators Panel. Bryson is one of the featured creatives to be found inside.

These days Bryson is an artist again. Paintings mostly. "People buy paintings. They don't buy performance art." The upcoming School of Art show, however, a mixture of performance and clothing that was and is meant to explore the theme of wanting to disappear and wanting to show off – the teenage Bryson in a nutshell, perhaps – is a lovely chance to reclaim a small part of her past, as well as being a reminder of the girl she was and the place she comes from. "Yes," she says when I suggest as much. "How brilliant is that?"

"It's going to be slightly different, reimagined," she says of the new version. Most importantly this time around she's going to get the chance to film it.

Back in 1981 Bryson's show was pure pop art. Pop life was just around the corner.

Bryson was a girl from Shawlands who was fired up by punk and for a short time became a pop star in the mid-1980s, as famous for her polka-dotted image as the sweet, sharp songs that became the trademark of the band before it fell apart under industry pressure and personal differences.

The dressing up – a combination of her mother's cast-offs and charity shop bargains, heavy make-up and serious backcombing - began long before the band. Punk was the inspiration. The movement represented freedom and excitement, she says now. "Before that I loved music but I didn't feel part of it or connected to it.

Dressing up was an act of defiance. "Growing up in Glasgow as a teenager in the seventies I found it really intimidating to be a young woman where people shouted at you or made comments about you, good or bad," she adds. "I didn't want to be judged on my appearance. When punk came along it was a fantastic opportunity just to be in control of your own image and not conform. People would look at you, but they'd be looking at what you chose to put on rather than at you.

"I'm not sure what it's like now but as a young woman you were fair game to be judged on a daily basis when you're just going about your business. It's really intimidating to be shouted at. I would rather people shouted at me because I was making a statement rather than just walking around being me."

The punk scene in Glasgow was tiny but through it she met McDowall. "We were hanging out in the same crowd. Everyone was in a band in Glasgow at that point. It was an unwritten rule."

Punk proved therapeutic too. The desire to be part of the scene pushed her to go out into the world. Frankly, that was one of her greatest achievements. At the age of 15 she had become severely agoraphobic and didn't leave the house for a year.

"It's anxiety and depression really," Bryson explains, "but it manifests as you're terrified to go out. But I was terrified to stay in as well. I was just terrified generally because you're so anxious. The anxiety level becomes crippling and, of course, back then there was not so much written about it so I did not have a clue what was happening.

"I thought I was dying basically. I remember thinking 'I'm never going to feel the same again. Something's changed in my head and I'm never going to feel good again.'"

"It affected me up until I was about 40. From about then it got better. Naturally you have periods of depression and you come out of it. I could do things. But generally I had to do things with other people. I wasn't very independent."

Strawberry Switchblade's debut single Trees and Flowers was Bryson's response to her illness. The band formed in 1981. It started as a four piece band but before long they reduced down to a duo. They got attention almost immediately. "I missed my degree tour because I was touring," Bryson recalls.

By the end of 1984 they were on the cover of Smash Hits and their single Since Yesterday entered the top ten at the start of the following year. Their Gothic Lolita look also went down well in Japan. But the inevitable move to London proved isolating, the friends began to grow apart and pressure from the label killed the joy for Bryson.

"You are a commodity when you're signed to a large record company. They want their return. They want you to make them money and there's not an awful lot of nurturing. So, if you're not getting on with the person you're supposed to be in a creative partnership – and we weren't really getting on – it's not comfortable in any way. You really do need to have a united front as a band just to protect yourselves so if you're not it's not good."

The band's final days burned her a bit, she admits. But by the early 1990s she was a mother and besotted with the experience. It was only when Jessie went to school that she decided to resurrect her artistic career.

Does it bother Bryson that her short time in Strawberry Switchblade remains the thing people know her for? "No, not at all. It's just part of my life and I'm quite happy about it. It was fairly short-lived so only people of a certain age will remember. My friend's kids think it's hilarious. They look it up on You Tube and go 'oh, it's you."

She's been in London since the 1980s but now and again, she says, she toys with the idea of moving back to Glasgow. It has changed so much. "In the seventies I found it to be quite bleak. There wasn't an awful lot to do. It wasn't pretty. The buildings were covered in black soot. It was a really dark, dour place. It didn't seem to be as creative as it could be and is now. It's been wonderful to see it emerge. Because it's a beautiful city to look at.

"What I find really strange," she adds, "is you bump into people with maps now. Actual tourists asking you directions. The very idea. [In the 1970s] If we met someone from England we thought that was exotic.

"One of the gang who went to punk gigs we called him London because he said he was from London and he had a London accent. How cool. Turns out he was from Castlemilk."

Jill Bryson's performance installation takes place at the Glasgow School of Art on Wednesday, November 30 to accompany the launch of Inventors of Tradition II, edited by Catriona Duffy and Lucy McEachan, priced £38. Visitwearepanel.co.uk for more details