Bagley played for Boston College for three seasons, where he averaged nearly 18 points a game and became the first Eagle to earn Big East Men's Basketball Player of the Year honors. He averaged 20.4 points per game during the 1980-81 season, his sophomore year, and led the Eagles to the regular-season championship and NCAA Tournament's Sweet 16. The following year, Bagley scored 21.1 points per game and led Boston College to the Elite Eight of the NCAA Tournament. Bagley also played in the Men's World University Games in 1981, and led the team with 14.8 points per game. He left Boston College after his junior year and entered the 1982 NBA Draft. He was inducted into the Boston College Varsity Club Athletic Hall of Fame in 1995.