Bouchard was born in Montreal, Quebec, Canada, on September 4, 1919. He grew up during the Great Depression and didn't have the opportunity to play hockey until he was 16 years old. He learned to skate on rented skates and borrowed $35 from his brother to buy a complete set of hockey equipment.

Bouchard began his professional hockey career with the Verdun Maple Leafs of the Quebec Senior Hockey League in 1940. He was signed by the Montreal Canadiens in 1941 and made his NHL debut that same year.

Bouchard was a physical defenceman who was known for his strong skating and his ability to break up opposing plays. He was also a skilled passer and a threat to score from the point.

Bouchard was a key member of the Montreal Canadiens' dynasty of the 1950s. He won the Stanley Cup four times with the Canadiens (1953, 1956, 1957, and 1958) and was named to the NHL First All-Star Team three times (1945, 1946, and 1947).

Bouchard retired from hockey in 1956. He was inducted into the Hockey Hall of Fame in 1966.