Nicky Bissett was born in Fulham. He worked as a gas service engineer and played football for Hornchurch and Walthamstow Avenue of the Isthmian League and Conference clubs Dagenham and Barnet who set a record for a transfer between non-league clubs when they paid £20,000 for his services in March 1988.
Six months later, Second Division Brighton & Hove Albion broke the record for a non-league player when they paid Barnet £125,000 for Nicky. He became a regular in the team over his first 18 months, but he suffered a badly broken leg in a match against Swindon Town that kept him out for nearly a year. He returned in time to help Albion reach the 1991 Second Division play-off final, which they lost to Notts County, but broke the leg again in 1993 and suffered a knee injury the following year which effectively finished his professional career.