He attended Sacred Heart Roman Catholic School in Leeds. He was introduced to rugby league in 1945 when he played for his school immediately after the end of World War II.
He signed professional forms for Hull in 1953, but never played in the first team. He was transferred to Dewsbury in 1957 and returned to play amateur rugby league in 1964, having played eleven seasons as a professional.
He coached amateur rugby league sides Stanningley, Dudley Hill, Milford[disambiguation needed] Marlins, Oulton Welfare, Castleford Lock Lane, Blackpool Borough, Dewsbury Celtic, Greetland All-Rounders, Mirfield, Oxford University and Yorkshire County.
In 1972 he returned to the pro-game as assistant coach at Dewsbury and began a new career as coach. He had spells as coach at Leeds and Dewsbury (twice) and three times for Bramley. He also enjoyed time at Wigan, Halifax, Bradford Northern, Workington Town, York, Keighley, Prescot Panthers, and Lancashire Lynx.
His career also included a three-year stint as Great Britain coach between 1984 and 1987 with test series against Australia, New Zealand and France. His term as coach of the national side also included the formation of the Great Britain under-21 team. He was succeeded as Great Britain coach by Malcolm Reilly.
During the 1986 Ashes series between Great Britain and Australia on their 1986 Kangaroo tour, Bamford came in for heavy criticism from a number of former Great Britain and England internationals for his selections of both the first and second test teams. After the Lions lost the first test 38-16 at Old Trafford in Manchester, many expected mass changes to the team for the second test. However, the only change came when centre Ellery Hanley was ruled out with injury and was replaced by St Helens winger Barry Ledger. The Lions lost the test and the series as the Kangaroos ran riot, running in six tries to one in a 34-4 hiding at Elland Road in Leeds. Garry Schofield scored the only try for the home side which came when Michael O'Connor dropped a low pass from fullback Garry Jack. At no other time in the game did the Lions look like scoring. Five changes were made to the team for the third test at Wigan's Central Park with the result being closer than many predicted, though the Australian's completed a clean sweep defeating Great Britain 24-15. Many English fans believed that French referee Julien Rascagneres allowing a contentious try to Kangaroos captain Wally Lewis midway through the second half ended any hope of the Lions snatching an unlikely victory.
Bamford was coach of Wigan between May 1981 and May 1982 before being sacked. Between November 1983 and February 1985, he was coach of Leeds.
In 1985, Bamford was the first ever appointed full-time Development Officer for rugby league in the UK when he served for the Leeds City Council Leisure Services for two and a half years.