Son of rugby league legend Gus Risman, Bev played rugby union at fly-half for the English national side (8 Test appearances) and for the British Lions (4 Test appearances). His international representative debut was made in 1959 for England against Wales. His last international rugby union appearance was in 1961.
After retiring he became involved in coach education, the development of the game in the South of England and the organisation of student rugby league. He was inducted to the rugby league Roll of Honour in 2005, and was elected President of the Rugby Football League in 2010. He was replaced by Jim Hartley in 2011.