He played for South Melbourne between 1968 and 1976, playing 178 games and kicking 325 goals. He was the Swans' Best & Fairest on five occasions, leading goalkicker three times and in 1970 he won a Brownlow Medal as the league's best and fairest player. He played for the Swans as a rover but was also thrown forward to kick a goal when they needed it. He was South Melbourne's captain from 1973 until his departure in 1976, when he transferred to Carlton. He played at Carlton until mid-1978, then transferred back to Port Melbourne.[4]
Bedford was also a talented batsman and leg-spin bowler for Victoria, playing 39 matches for the State between 1966–67 and 1972–73. He made 1602 runs at 28.10 and took 45 wickets at 33.40. His top score and only century was 134 not out against Western Australia in Melbourne in 1969–70, and his best bowling figures came later in the same season against South Australia in Adelaide when he took 5 for 40 in the second innings to help Victoria win and clinch victory in the Sheffield Shield. He played district cricket for Melbourne (ten seasons) and Carlton (one season).[6]
Bedford was selected in the Port Melbourne Team of the Century. He was inducted to the Australian Football Hall of Fame in 1999 and was named in the Swans team of the century which was announced on 8 August 2003. Bedford's father, William, was also selected in the Port Melbourne Team of the Century, and his nephew Stephen Allender won a J. J. Liston Trophy with Port Melbourne.[7]
Western Australia 26.18 (174) defeated Victoria (VFA) 5.11 (41), at North Hobart Oval, 9 June 1966, crowd: 20,047 Tasmania 19.27 (141) defeated Victoria (VFA) 7.11 (53), at North Hobart Oval, 11 June 1966, crowd: 23,764 Victoria (VFL) 14.17 (101) defeated Victoria (VFA) 9.7 (61), at North Hobart Oval, 13 June 1966, crowd: 13,969 South Australia 21.20 (146) defeated Victoria (VFA) 9.11 (65), at North Hobart Oval, 16 June 1966, crowd: 10,199
