Ron Bishop took up archery in 1955 as an activity in which he could partake alongside his wife. He first represented Great Britain at the World Championships in 1961, and went on to do so six more times in 1963, 1965, 1971, 1973, 1981, and 1983. He also took part in the European Championships in 1970 and 1972 and made the Olympic squad once, in 1972, where he placed 45th in the individual event. He continued to compete until the age of 72. At the time of his Olympic appearance he was competing for the Sefton Hospital Archers, but he joined the Nethermoss Archers in the mid-1990s, where his wife served as club secretary.
Great Britain