Bourque contested his first World Cup race in November 2002, a few days after his 18th birthday. On February 20, 2005, he finished third in the Super-G in Garmisch-Partenkirchen , making it onto the podium for the first time. His best World Cup results were second places in the giant slalom on December 21, 2006 in Hinterstoder and on March 3, 2007 in Kranjska Gora . At World Championships and the Olympic Games, Bourque was four times in the top ten. The best result he achieved was fourth in the giant slalom at the 2006 Winter Olympics in Turin , where he had achieved the fastest time in the first round.
At the end of November 2008, Bourque suffered a cruciate ligament rupture while running in before downhill training in Lake Louise , which is why he could not contest any more races for the rest of the 2008/09 season. The next season also ended early for the Canadian. On December 18, 2009 he suffered another cruciate ligament tear in the Super-G in Val Gardena without a fall. The 2010/11 season had to end Bourque again early. In January he tore the third cruciate ligament during training. After not contesting any races in the 2011/12 season, Bourque announced his retirement in the summer of 2012.