Rivard made his professional hockey debut with Toledo-Indianapolis of the International Hockey League in 1960-61, where in his rookie year he registered 45 points. The 1961-62 season marked a return to Indianapolis for Rivard before becoming a member of the International Hockey League's Fort Wayne Komets for the next four seasons.

From 1962 to 1966, Bob Rivard was a member of the Fort Wayne Komets where he was a two-time Turner Cup Champion in 1963 and again in 1965. An IHL First Team All-Star in 1965 and Second Team All-Star in 1966, Rivard won the Leo P. Lamoureux Memorial Trophy as the IHL's Top Scorer in 1966 before joining the Quebec Aces of the American Hockey League the following year.

After a strong season with the Aces that saw Rivard capture the Dudley "Red" Garrett Memorial Award as the AHL's Top Rookie, the Pittsburgh Penguins claimed him in the 1967 Expansion Draft.

1967-68 marked the Bob Rivard's debut in the NHL with the Pittsburgh Penguins. In 27 games with the team, he tallied 17 points while spending the other half of the season with the AHL's Baltimore Clippers.

Prior to the 1968-1969 season, the Penguins loaned Rivard to the Philadelphia Flyers before he returned to the Aces line up at the start the season. Although he began the season with the Aces, Rivard returned to the Clippers midway through the season.

Traded by the Penguins to Baltimore in 1969, Rivard spent the next five and a half seasons with the Clippers, leading them to the 1972 Calder Cup finals where they fell short against the Nova Scotia Voyageurs. Rivard returned to the IHL and the Fort Wayne Komets where he had won two Turner Cups midway through the 1974-75 season.

Bob Rivard retired from the game of hockey after his 1975-76 season with the Lindsay Lancers of the Ontario Hockey Association Senior "A" Hockey League.