After graduating from the University of New South Wales in 1976, Bruce Keller wrote and performed stand-up comedy in Sydney before moving to Melbourne in 1979. In 1980 he co-founded the Australian Nouveau Theatre (ANT), with Jean Pierre Mignon, and the following year he was a foundation member and worker with Mignon and Julie Forsyth for Anthill Theatre, South Melbourne. He returned to Sydney in 1987 and in that year was dramaturg for the Sydney Theatre Company's production of The Rivers of China.
In 1985 he wrote the children's play Puppy Love which he performed throughout Australia until 1987. Since then, the play has been produced both within Australia and overseas in Hong Kong (in Cantonese) and Canada. In 1989 he wrote Monkey See, Monkey Do whilst dramaturg-in-residence for Toe Truck Theatre (Sydney). The play has been produced throughout Australia and by Chung Ying Theatre Co. in Hong Kong (in Cantonese).
Keller also worked as an actor with the South Australian Theatre Company at the Adelaide Festival and with the Jigsaw Theatre Company in Canberra.