Bruce was named All-Southeastern Conference in 1986 and 1987, All-America in 1987, and Citrus BowlMVP in 1987. He first garnered national attention in a nationally-televised game in 1987 against Georgia Tech by intercepting three passes and returning one for a touchdown and making 10 unassisted tackles. Entering the NFL Draft, he was saddled with expectations of becoming the next Lawrence Taylor, though once drafted was described as "unquestionably the least heralded No. 1 draft choice this decade." He graduated from Auburn in 1988 as an education major.
Bruce was drafted with the first overall pick in the 1988 NFL Draft by the Atlanta Falcons. Although he was the first overall pick, Bruce started only 42 games in his 11-year career. Bruce enjoyed his most prominent role on the Falcons 1991 playoff team when he saw spot duty on offense as a tight end as well as defense. He signed with the Los Angeles Raiders as a free agent in 1992 and finished his career with the organization. Bruce played in 151 games over his 11-season career, posting 32 sacks and 4 interceptions. He was quite serviceable in Oakland but never lived up to the high expectations and was regarded as a bust.