Bence began his career as an apprentice with Brighton & Hove Albion, turning professional in May 1967. He had previously captained Sussex Schools Under-15 side. His league debut (and only league appearance for Brighton) came as a substitute the following season. In June 1968 he left for Reading, but was only to make 14 league appearances, scoring twice, in the next two seasons at Elm Park. In July 1970 Reading released the player and he joined Brentford, where he established himself, making 244 league appearances over 7 seasons and scoring 6 goals. In November 1976, having lost his place at Brentford, he played five league games on loan at Torquay United.
He left Brentford in March 1977, subsequently becoming player-coach at Wokingham Town and putting to use the FA coaching qualification he had gained in 1973. He was later youth coach at Queens Park Rangers and coached at Farnborough Town. In August 1984 he was appointed manager of Wycombe Wanderers, and guided them to promotion to the Alliance Premier League in his first season in charge, but only because the two teams finishing above them failed the ground grading criteria. Wycombe were relegated the next season, though Bence had already left in January 1986 because of increasing work commitments.