Garry Bauman was born in Innisfail, Alberta, south of Red Deer. He played youth hockey in High River, but was initially a forward. Forced to don the pads after the team's regular goalie was unable to play, Bauman posted a 5-0 shutout. He never left the crease from that point on.
Bauman would play his junior across the provincial border, starring for the Prince Albert Mintos in the Saskatchewan Junior League. But Garry Bauman was not going to proceed through the usual route to the NHL. Rather than graduating to higher levels of junior hockey, he was more interested in pursuing his education. He took a scholarship to play at Michigan Tech University.
From 1961 to 1964 Bauman was one of the most dominant goaltenders in the history of college hockey. He was never more dominant than in his first season, 1961-62, Bauman posted a 24-1 record in 25 games, leading the Huskies to the NCAA national championship.
Bauman turned pro in the Montreal Canadiens organization, playing a minor league season in Omaha before two dominating seasons in Quebec City.
In the 1966-67 season he made a two game appearance with the Habs. Bauman was called up on to make emergency appearances thanks to injuries to Gump Worsley and Charlie Hodge. Bauman went 1-1, allowing five total goals.
Expansion came in 1967-68 and Garry Bauman joined the Minnesota North Stars as Cesare Maniago's back up, though it was Bauman who started the North Stars first ever game. That game, against expansion cousin St. Louis Blues, finished in a 2-2 tie. Bauman would play in 26 games with the North Stars, though his 4-13-5 record was rather uninspiring, but it was enough to see him represent Minnesota at the NHL All Star Game.
Bauman did return for seven more games (0-2-1) the following season and then all but retired. He resurfaced in Calgary to play several seasons of senior hockey.
After leaving the ice Bauman returned to small town Alberta. He became a math and sciences teacher at a high school in Okotoks, just south of Calgary. He taught until retiring in 1999.
Garry Bauman passed away from cancer in 2006.