Rush was educated in Melbourne at Wesley College and Toorak Teachers' College. He completed a Bachelor of Education at Deakin University in 1985, and worked as a teacher in rural areas for many years. Rush began writing poetry in the early 1960s, and his first published poem was 'A Penny A Pan' in a Teachers' Union Journal in the late 1980s. His work has also been published in the Australian and the Australian Financial Review.

Rush moved to the Huon Valley in Tasmania in December 1993, and became the ABC's Country Hour poet, and a regular storyteller and poet on the Sunday programme. He also wrote a thirty-episode radio serial 'Yendara' that was broadcast by the ABC in 1995.