Born in Neufchatel, Québec, Bédard competed in here first biathlon event at age 15, and became Canadian junior champion in the sport in 1987.
In 1991, she became the first Canadian to win a biathlon World Cup event, and she formed part of the Canadian team at the 1992 Winter Olympics, held in Albertville, France. It was the first time that women competed in biathlon at the Olympics, and Bédard won a bronze medal in the 15 km.
The following year, she won her first major title, as she won the 7.5 km event at the World Championships, also placing second in the 15 km race. At the 1994 Winter Olympics, she improved this performance, and won both individual events.
She briefly retired from the sport to give birth to her daughter (the father was another biathlete, Jean Paquet). Her return was not very successful, being hampered by injuries. After the 1998 Winter Olympics, Bédard retired from the sport. She later announced to try to make the Canadian Olympic team as a speed skater, but did not pursue this goal for long.