College - Shawn played four seasons with the Boston University Terriers. In his four years he helped lead the team to the Frozen Four each year. Bates' teams appeared in two NCAA Finals and won the NCAA Championship in 1995, Bates was named to the All Tournament team. Overall, Bates compiled 73 goals, 71 assists, 144 points, and 190 penalty minutes in a total of 160 games.
NHL - Shawn was drafted by the Boston Bruins in the 1993 NHL Entry Draft, 4th Round, 103rd Overall. After four years with the Bruins, he was signed as a free agent by the Islanders on April 8, 2001. Bates is remembered most for scoring on a penalty shot in Game 4 of the Islanders' Eastern Conference Quarterfinal playoff series against the Toronto Maple Leafs. Bates beat Maple Leaf goaltender Curtis Joseph top shelf to give the Islanders a 4–3 lead with 2:30 to go in regulation, and the Islanders went on to win the game and tied the series 2–2. The penalty shot was the third playoff Penalty Shot in Islander history and the first to be successful. He was placed on waivers by the Islanders on June 27, 2008 and ultimately had his contract bought out.
In the 2002–03 NHL season, Bates led the NHL with six short-handed goals.