He was chosen 104th overall by the Montreal Canadiens in the 1988 NHL Entry Draft and was assigned to the Sherbrooke Canadiens of the AHL for seasoning. In 1989-90, he recorded a fine 21-8-7 mark and led the league with a 2.74 goals against average. Bergeron was placed on the AHL first all-star team, was presented the Aldege "Baz" Bastien Memorial Award as the league's best goaltender, and shared the Harry "Hap" Holmes Memorial Award with teammate Andre Racicot for allowing the fewest goals in the league.
The young netminder posted a 3.76 goals against mark and a 7-6-2 record for the Habs in 1990-91 but was unable to gain a permanent spot as Patrick Roy's understudy. In June 1992 he was given a new lease on life when he was traded to the expansion Tampa Bay Lightning. He played 21 games for the first year club but slid down the depth chart after the club acquired Daren Puppa prior to the 1993-94 season.
Bergeron starred for the International Hockey League's Atlanta Knights in 1993-94 when he won 27 games and shared the James Norris Memorial Trophy for allowing the fewest goals in the league with Mike Greenlay. He signed as a free agent with the Los Angeles Kings in 1996 but spent most of the 1996-97 season in the IHL with the Phoenix Roadrunners before retiring.