She says the city made her famous - and fat.
"I came to the city to make it big," she says, adding with a snort of laughter: "Well, I was VERY big. Sixteen stone at one point."
Diet is one of the subjects the multi-talented performer discusses in a new BBC film, I Belong to Glasgow.
The four-part series, which starts on June 27, will also feature Alex Norton, Elaine C Smith and Sanjeev Kohli.
Dunbar also tackles football, which she cheerfully admits she knows nothing about, leads a singsong in Central Station and explores the city's lesbian and gay culture.
But while it is all very lighthearted, she admits watching the film for the first time was an unexpectedly emotional experience.
"I was surprised by how moved I was," she says. "My dad died in April, and talking about my childhood - well, it made me feel emotional and glad at the same time, which sounds like a strange mix. My dad watched all my shows, he was always there."
There is a moment in the film when Dunbar reveals a message she wrote in her diary when she was 10.
"I, Karen Dunbar, swear one day to be on TV...world look out, here I come...I will 'forfill' this..." it says.
She smiles: "I always wanted to be on telly. One of my earliest memories was age four, belting out Que Sera Sera on stage in the Labour club my dad took me to and he was watching me and clapping. It's a very evocative, powerful memory."
Dunbar grew up in Ayrshire but loved visiting Glasgow, "the golden city over the hill". She admits she moved away from home as a teenager partly to escape prejudice and homophobia.
"Once they took my cat, drowned it and left it in my garden with a note saying "you f****** lesbian," she recalls.
"I don't think I really ever got over that."
She added: "Glasgow was a place of safety for me - there were pubs where you could spend time without fear of homophobia. The city accepted me for who I was."