Bourbonnais was introduced to racing by his father, a snowmobile racer, and began competing on Canadian national circuits in 1983. He started in the Formula 125 superkart series, finishing fifth in the Quebec championship standings after scoring several podium finishes. He dominated the following season, winning all but two races and winning the Formula 125 race supporting the 1984 Canadian Grand Prix at Circuit Gilles Villeneuve.
Bourbonnais transitioned to Formula Ford 2000, finishing second at Circuit Trois-Rivières in his debut season in 1985. He improved to third in the championship standings in 1987, winning at Mont-Tremblant. Bourbonnais then became a double champion, winning six out of eight races in 1988 and six out of nine races in 1989. In 1988, he also won the SCCA National Championship Runoffs in Formula Continental, becoming the first driver to do so in a Formula Ford 2000 chassis.
After his 1988 success, Bourbonnais stepped up to the Formula Atlantic series. He won from pole position at his debut at Lime Rock Park in 1989, finishing third in the final standings. He improved the following year, winning two races at Heartland Park Topeka and Lime Rock Park, ultimately finishing second in the championship standings.
Bourbonnais attempted to race in the International Formula 3000 Championship in 1990, but failed to qualify for either race at the Bugatti Circuit or Circuit Paul Armagnac. In 1991, he raced for Courage Competition in the World Sportscar Championship, finishing tenth overall at the 430 km of Monza and retiring after 293 laps at the 24 Hours of Le Mans.
In 1992, Bourbonnais raced in both the Atlantic Championship and British Formula 3000, finishing thirteenth at Montreal and seventh at Trois-Rivières in Atlantic, and third at Donington Park in British Formula 3000 before leaving the series due to a lack of sponsors. He returned to the Atlantic Championship in 1993 with Player's cigarettes sponsorship, winning seven races but finishing second in the championship to David Empringham by only four points.
Bourbonnais made his debut in the CART series in 1994 at the Grand Prix of Long Beach with ProFormance Motorsports, retiring after 24 laps with a broken exhaust. He later raced for McCormack Motorsports, suffering a crash at Toronto and experiencing technical difficulties at Mid-Ohio, Vancouver and Road America.
Bourbonnais ran a partial season in Indy Lights in 1995, scoring a second place at New Hampshire International Speedway. He ran a full season in 1996, earning a pole position at Nazareth Speedway and winning at Vancouver, finishing fourth in the championship. He ran a partial season in 1997 with Eclipse Racing without notable results.
Throughout his career, Bourbonnais attempted the Indy 500. In 1997, he qualified in 32nd place but retired after nine laps due to an engine failure. In 1998, he failed to qualify, unable to beat Johnny Unser’s time on Bump day.
Beyond open-wheel racing, Bourbonnais raced in sportscars and GTs. In 1998, he finished tenth overall and eighth in class at the 6 Hours of Watkins Glen in a Ferrari 333 SP. In 2003, he replaced Paul Gentilozzi at Rocketsports Racing for a one-off Trans-Am Series race at Trois-Rivieres, qualifying third and finishing fifth.
In 2018, Bourbonnais began a career in politics, running as a candidate for the Coalition Avenir Québec in the 2018 Quebec general election in Vaudreuil, finishing second.
[unverified] Bourbonnais's early karting career saw him dominate the Quebec championship before transitioning to formula cars.