Bradmore was recruited to the VFL from Sydney club North Shore and spent most of his time in the Footscray reserves. A key position player, he played at West Perth for the rest of the 1980s. He won the Breckler Medal, West Perth's 'fairest and best' award, in 1985. Also that year, he represented Western Australian in an interstate match against South Australia at Subiaco. Bradmore also made interstate appearances for New South Wales in the 1988 Adelaide Bicentennial Carnival. In 2015 he played a year of senior football for the Grafton Tigers playing 14 games in the NCFL.
South Australia 30.18 (198) defeated Western Australia 16.15 (111), at Subiaco Oval, 15 June 1985
Victoria 19.16 (130) defeated Western Australia 9.11 (65), at Subiaco Oval, 16 July 1985
Semi-Final: South Australia 12.8 (80) defeated New South Wales 8.11 (59), at Football Park, 3 March 1988 3rd Play-Off: New South Wales 10.8 (68) defeated Western Australia 9.12 (66), at Football Park, 5 March 1988