The native of Waterloo, Ontario grew up in a sports-oriented family. His brother Bobby went on to star with the Boston Bruins. David was a supreme athlete who likely would have made a successful professional. At he the age of 16 turned down a spot on the Bruins' Boston Olympics farm team to attend St. Michael's College and, later, the University of Toronto. During his student days he suited up for the Oshawa Generals when they won the Memorial Cup in 1944. At this point in his life Bauer decided that his calling was as a Basilian Priest.

Following his ordination in 1953, Bauer returned to St. Mike's as a teacher and the coach of the junior team. He guided the school to the Memorial Cup in 1961 and developed many players who went on to the Toronto Maple Leafs including Frank Mahovlich and Dave Keon.

Following the Memorial Cup win, Bauer took a position at St. Mark's College at the University of British Columbia. It was during this time that he began to think seriously about putting together a national team of the top amateurs from across Canada. He presented his idea at the annual meeting of the Canadian Amateur Hockey Association in 1962 and it was accepted. He populated his roster with UBC students, some of whom had followed him from St. Mike's.

The first test of the national team came at the 1964 winter Olympics in Innsbruck, Austria. Bauer's influence was vividly evident at this tournament. The Canadians finished fourth on goal difference but competed passionately and as a close-knit unit. Future NHL regulars on the squad included Brian Conacher, Rod Sieling and Marshall Johnston.

One incident stood out as measure of the Canadian coach's character. During a game versus Sweden, one of the opposing players cross-checked a Canadian skater, broke his stick and threw the handle at the bench, striking Father Bauer in the forehead. The enraged Canadian players were about to jump over the bench when they were stopped by one sharp command from their coach. The next evening, Bauer invited the Swedish player to watch a hockey game with him. Following the competition, the Canadian coach was presented a gold medal for exemplary leadership.

Bauer was on hand at the 1968 games as manager when Jackie McLeod coached the Canadian entry to the bronze medal in Grenoble, France. Despite having such future NHL regulars as Gerry Pinder, Billy MacMillan and Wayne Stephenson, Canada was overmatched against the Soviets and Czechoslovaks who were able to ice their best players.

Between 1969 and 1979, when Canada withdrew from international hockey because it was not allowed to use its best NHL players, Bauer shared his knowledge with lesser hockey playing nations. He avoided the national team program at this time because he vehemently opposed the use of professionals at the Olympics. During this period he travelled to Japan twice a year for six weeks of instruction. His on-ice expertise and outlook on personal growth through sports was readily accepted in the disciplined Japanese culture. In 1973 he went to Austria for a year at the request of the Austrian Ice Hockey Federation, which feared that its national team would be demoted from "B" to "C" pool. He led the Austrians to a fifth place finish at the "B" pool championships that year which allowed them to keep their place in that level of competition.

When Canada returned to the Olympics at Lake Placid in 1980, Bauer worked as the squad's managing director. The team finished a disappointing sixth but sent Glenn Anderson, Paul MacLean and Randy Gregg to the NHL. A steadying influence on the young defense corps was Terry O'Malley, a veteran of the first national team in 1964.

Between 1963 and 1969 Bauer worked to implement a national junior team. Canada's withdrawal from international hockey damaged the program for much of the 1970's. However, Canada's re-emergence at the 1977 World Championships and the 1980 Olympics, Father Bauer was able to persuade Hockey Canada to approve a training camp a few months before the world junior championship.

In 1981 Bauer was appointed the vice-president of Hockey Canada and the chairman of Canada's Olympic program. He also continued to teach at St. Mark's and help out with the UBC hockey program.

In the years just before his passing in 1988, Father Bauer was accorded a multitude of honours reflecting his importance to the game. These included the Order of Canada (1967), having an arena named after him in Calgary to serve as the home base of the national team (1986) and a bursary in his name at St. Michael's College (1987).

Father Bauer was elected into the Hockey Hall of Fame in 1989.