The Bruins drafted Bob Sweeney out of high school in the U.S. in 1982. He went on to play at Boston College for the next four years before making his NHL debut with Boston in the 1986-87 season but spent the majority of the year with the teams AHL affiliate in Moncton.
The 1987-88 season was Sweeney's first full year in the NHL, a year that saw the Bruins go all the way to the Stanley Cup finals only to be swept by the Oilers. Two seasons later, they were back in the finals against Edmonton, this time winning one game but giving Lord Stanley to the Oilers once again.
After six seasons as a Bruins forward, Sweeney was claimed off waivers by the Sabres in 1992 and remained with the team for three seasons. The Islanders claimed him once again in the 1995 Waiver Draft, but during the 1995-96 season Sweeney was dealt to the Flames, where he finished his NHL career.
He spent the next season in the IHL before heading overseas to play in Germany in 1997 where he played in the German Elite League until 2001.