He played in Sønderborg Boldklub as a youth player. When serving conscription he moved to Aarhus and joined the local side AGF Aarhus. He won the 1960 Danish championship and 1965 Danish Cup with AGF. When AGF met Scottish club Celtic F.C. in the European Cup Winners' Cup in 1965, Bent Martin impressed the management of Celtic to such a degree that they signed him. Bent Martin joined Celtic from AGF on February 4, 1966. His only first team appearance for the club was in a Glasgow Cup match.
Martin left Celtic on December 23, 1966 in order to join league rivals Dunfermline Athletic on a transfer fee of £3500. He won the Scottish Cup with the club in 1968. In May 1970, Martin moved to Rapid Vienna in Austria, before ending his career playing for AGF in the 1973 season. During his last season he was called up for the Danish national team for a game against Norway in June 1973 but he turned down this opportunity because he was to pass an exam at a banking school on the day of the match.
After retiring, Bent Martin has had various coaching spells such as briefly managing Viborg FF, and serving ten years as a goalkeeping coach in Aarhus Fremad. Since his retirement from football, Bent Martin has had a career in banking in Denmark.
- Mogens Weinreich, Bankmanden med målmandshandsker, aarhus.dk, February 18, 2003.
- Henrik Stanek, Filialchefen spillede med Alex Ferguson, finansforbundet.dk, November 30, 2006.
- Martin, Bent at thecelticwiki.com
- Bent Martin fylder 60, agffodbold.dk, February 19, 2003.
- AGF-målmand i Hall of Fame, aarhus.dk, March 2, 2007.[dead link]