A native of Fort William, Ontario, Bodnar played for the Fort William Hurricanes-Rangers of the Thunder Bay Junior Hockey League for three seasons from 1940-43. . He turned pro with the Toronto Maple Leafs in 1943-44, winning the Calder Memorial Trophy as the NHL's best rookie. Bodnar played 4 seasons with the Leafs and won 2 Stanley Cups (1945 & 1947). Bodnar was traded (with others) to the Chicago Black Hawks in 1948 for Max Bentley. He played seven years for the club before being traded to the Boston Bruins for Jerry Toppazzini in 1954. He retired in 1955.