Bonner became famous in the 1960s children's television series Skippy the Bush Kangaroo, later moving on to lead roles in the dramas Cop Shop and Skyways.

[citation needed] Bonner went on to appear in many Crawford Productions television series, including The Box, Matlock Police, Division 4, Cop Shop, Skyways, and Carson's Law.

[citation needed] His notable film roles include Eyewitness (1970), You Can't Win 'Em All (1970), Creatures the World Forgot (1971), Inn of the Damned (1975), The Mango Tree (1977), Money Movers (1978), The Man from Snowy River (1982), The Highest Honor (1983), Quigley Down Under (1990), Dead Sleep (1990), Hurricane Smith (1992), and Liquid Bridge (2003).

He has twice portrayed Australian World War I soldier Murray Bourchier, to whom he bears a remarkable likeness, in the 1987 film The Lighthorsemen and a 1993 episode of The Young Indiana Jones Chronicles.

[citation needed] In 2017 Bonner was appointed a Member of the Order of Australia for significant service to the performing arts as an actor, to surf lifesaving, and to the community through charitable organisations.