Bodger played his minor hockey with the Cowichan Midget Capitals before joining the Kamloops Junior Oilers of the Western Hockey League. In his first season with Kamloops, he scored 26 goals and 92 points, being named to the WHL Second All-Star Team. The following season, Bodger scored 21 goals and added 77 assists for 98 points, earning First All-Star Team honours. Both seasons he was named the team's top defenceman. With 190 points in two seasons of junior hockey, Bodger was one of the top prospects going into the 1984 NHL Entry Draft, being ranked the seventh greatest prospect by the NHL Central Scouting Bureau. As a top prospect, Bodger was expecting to be selected early in the draft. He had earlier conversations with the Detroit Red Wings, who told Bodger there was a "90 per cent chance" they would pick him at seventh overall, going so far as to ask he wear a red tie to match the team colours. However, the Red Wings instead chose Shawn Burr. Instead, the Pittsburgh Penguins made Bodger their second choice of the draft; they had selected Mario Lemieux, who would become one of the greatest players in NHL history, first overall. Bodger made his NHL debut alongside Lemieux on October 11, 1984 against the Boston Bruins. A shoulder separation limited his first season to 65 games, in which he had 5 goals and 26 assists. Bodger cited Lemieux, who led the team with 100 points, for helping him earn a lot of assists. The next season, he appeared in 79 games, scoring 37 points. Starting the 1988–89 season with the Penguins, Bodger was traded along with Darrin Shannon to the Buffalo Sabres on November 12, 1988 for Tom Barasso and a third-round draft choice in the 1990 draft. He played 61 games with the Sabres that season, scoring 7 goals and 40 assists, to make a total of 8 goals and 44 assists for the entire year. He would retire on December 14, 1999 with the Vancouver Canucks as the highest scoring defenceman from British Columbia.
Bodger played for Canada at three World Championships, in 1987, 1996, and 1999. Joining the Canadian national teamfor the first time in 1987, Bodger played in all ten games, scoring one goal and one assist as Canada finished fourth in the tournament. His next appearance in the World Championships was in 1996. In eight games, Bodger contributed three assists and was named the team's best defenceman as Canada won the silver medal. His third and final appearance for the national team was at the 1999 World Championships, where he scored three assists in ten games for the fourth place Canadians.
