Attended Cornell University
Dryden decided to play college hockey in the United States at Cornell University, where he received a college scholarship. He faced quality competition and was an outstanding college player. While earning his B.A. in history, Dryden was an All-American three times and had a goals against average of 1.65 in seventy-one games. Cornell won the Division I title in 1967; in 1969, it was second in Division I.
After Dryden graduated in 1969, Montreal sent him to play for Canada in the World Championships in Stockholm, Sweden, so he could gain more experience. Dryden played in two games, including a 1-0 shutout against the Americans. Dryden then signed a three-year deal to play for Canada's national team as a way of developing his goalie skills. Soon this contract was negated as the program was in turmoil, and he left the national team in the summer of 1970. Dryden also attended law school at the University of Manitoba during this time.
Dryden's next career move was to sign with the Montreal Canadiens. He was assigned to their minor league system, playing for the Montreal Voyageurs in the American Hockey League (AHL) for the 1970-71 season. His coach there, Floyd Curry knew he was good enough to play for the Canadiens—Dryden had proved it by playing well in an exhibition game. In thirty-three games with the Voyageurs, Dryden had a goals against of 2.68 and three shutouts. But hockey was not his only focus. Dryden also began attending law school at Montreal's McGill University.