Bobby Dollas was chosen 14th overall in the 1983 Entry Draft by the Winnipeg Jets. He made his NHL debut that season on October 5 in a 6-6 tie with the Red Wings before returning to his major junior team.
Dollas played midget hockey with Lac-St-Louis of the Québec AAA. In 1982-83, he joined the Laval Voisins and scored 61 points as a major junior rookie. That year, he was a QMJHL Second Team All-Star. After making his NHL debut at the start of the 1983-84 season, Dollas returned to junior and scored 45 points in 54 games for the Voisins. The Voisins were the QMJHL champions that year, but they failed to win the Memorial Cup, even with Mario Lemieux leading the team. That was the year he scored a record 133 goals and 149 assists for 282 points in 70 games.
In 1984-85, Dollas turned pro and played nine games at the NHL level. In 1985-86, he played 46 games for the Jets. After a year in the minors, he was traded on December 17, 1987 to the Québec Nordiques for Stu Kulak. That year he played nine games at the NHL level. In 1988-89, the total increased to 16 games.
After a year with the Canadian National Team, Dollas signed as a free agent with the Detroit Red Wings on October 18, 1990. He joined the Red Wings full-time that year and scored his first NHL goal on November 17 against the Maple Leafs' Peter Ing.
On June 24, 1993, the Anaheim Mighty Ducks in the Expansion Draft claimed Dollas. That year, he recorded a career-high nine goals. In the shortened 1994-95 season, he scored 20 points in just 45 games. In 1995-96, Dollas scored a career-high 22 assists and 30 points.
The 1996-97 season was a satisfying one for Dollas, who helped lead the Ducks into the post-season for the first time in franchise history.
In 1997-98, Dollas was traded on January 9 to the Edmonton Oilers for Drew Bannister. At the conclusion of the season, Dollas was traded with Tony Hrkac on June 16 to the Pittsburgh Penguins for Josef Beranek.
On November 9, 1999, Dollas signed as a free agent with the Ottawa Senators. After just one game with his new team, he was claimed on waivers by the Calgary Flames on November 11, where he played 49 games before signing as a free agent with the San Jose Sharks in November 2000. But he didn't last long there, either. He was dealt to the Pittsburgh Penguins on March 12, 2001.
Dollas won a gold medal with Canada at the 1985 World Junior Championships and was a tournament All-Star.