Bunton was born and grew up in Albury, New South Wales. His natural ability attracted the attention of all twelve VFL clubs, and he was eventually recruited by Fitzroy in 1930. However, he was unable to play during the 1930 season, after it was shown that Fitzroy had offered him a one-off £222 payment (about $25,000-30,000 in present day terms), which was illegal under VFL rules. His initial, legal match payments were the modest sum of £2 a week.
Bunton played as a rover/follower and achieved instant success, winning Brownlows in his first two seasons in the VFL. He worked in a department store during the day, and practised baulking by weaving his way through crowds of shoppers. One of his opponents, Dick Reynolds, spied on him during this activity in order to learn how to defeat his technique.
Bunton played 119 games for Fitzroy, kicked 209 goals, averaged over thirty kicks per match and won five club best-and-fairest awards, in addition to his Brownlows. He was appointed captain of Fitzroy in 1932 and was named Champion of the Colony that same year. He was runner-up for the Brownlow in 1934. While playing, Bunton also spent the 1936 season as senior coach at Fitzroy, but could only manage two wins. He was also Fitzroy's leading goalkicker in 1936 and 1937. Bunton polled 122 Brownlow Medal votes in his 119 games, averaging 1.03 votes per game. In the history of VFL/AFL, no other footballer has averaged over 1 Brownlow vote per game over their career.
Other state leagues were officially equal in standing to the VFL at the time, and although their finances were limited compared to Victorian clubs, the WANFL and the South Australian National Football League (SANFL) had the ability to attract players away from the VFL. At arguably the height of his career, in 1938, Bunton moved to Western Australia (WA), as the playing coach of Subiaco. He played 72 games and kicked 190 goals with the club, and won the Sandover in 1938, 1939 and 1941. Just as at Fitzroy, Bunton did not win a grand final during his senior career. During World War II, senior football competitions were reduced, officially or virtually, to junior competitions. Bunton returned to Fitzroy for a few games in 1942 and played his last senior games with Port Adelaide, in the South Australian National Football League (SANFL), during the 1945 season.
Bunton spent the 1946 season as an SANFL field umpire, before he was appointed coach at North Adelaide. Bunton spent the 1947 and 1948 seasons with North, but was unable to take the club to the finals.
His son, Haydn Bunton, Jr., made his playing debut in 1954, at North Adelaide and went on to become an accomplished footballer and coach in his own right, himself winning the Sandover Medal in 1962 with Swan Districts.
Haydn Bunton Senior died as a result of a car accident in 1955. In 1996, he was named at left forward pocket in the AFL Team of the Century, and was made an inaugural "Legend", in the Australian Football Hall of Fame.
During his playing career, Bunton was considered by fans of the sport as a player of integrity, who rarely if ever engaged in unduly rough play. His fame was enhanced by him having his own radio show on 3DB, and a Melbourne newspaper column, when he played with Fitzroy. He later had radio programs in Perth and Adelaide. He was regarded as a sex symbol in the 1930s, and his looks were compared to those of film star Rudolf Valentino.
Bunton's ability to excite spectators during the 1930s, and relieve them of the misery of the Great Depression, invite comparisons with cricket superstar Donald Bradman and the much-loved racehorse Phar Lap. There are other similarities with Bradman: Bunton and Bradman once played together in a New South Wales Country cricket team, and in the early 1930s, Bunton was regarded as a possible Test cricketer.
While he was with Fitzroy, a young Aboriginal footballer named Douglas Nicholls was signed by the club. Bunton immediately befriended the diminutive yet skilful South Australian, a significant gesture considering race relations at the time..