As a director she has created Amada, Roadkill, Grit: The Martyn Bennett Story, Glasgow Girls and Room.
[1] The band received favourable write-ups[2][3] with the Scottish music press making Bissett a cover star.
[5] In 1995 she was the singer in the band, Swelling Meg, a three-piece "comprising acoustic guitar, bowed double-bass and Bissett's athletic voice".
[11][12] Roadkill, was a 2010 Edinburgh Festival Fringe show devised by Bissett and Stef Smith about sex trafficking.
[14] In 2011 she conceived the musical Glasgow Girls with book by David Greig about a group of activists who took up an ethical fight against the deportation of asylum seekers who had settled in Scotland.
[19] Grit: The Martyn Bennett Story was created by as part of the 2014 Commonwealth Games cultural programme.
[23] In addition to directing, Bissett co-wrote the music for a stage version of Emma Donoghue's book Room, with Kathryn Joseph.