Championships twice, Wimbledon four times, and the U.S. Nationals eleven times. His best showing at a grand slam event was reaching the round of 32, which he did once at both Roland Garros and Wimbledon, both in 1954, and four times at Forest Hills, in 1955, 1956, 1959, and in 1961. Despite having a very limited time in tennis play, in many years playing tournaments only in the summer months, Bédard was an outstanding clay court player, with 30 tournament wins against many well-known clay specialists. During his career, Bédard defeated No. 1 players of 20 different countries, including Australia (Adrian Quist, Roy Emerson), the U.S. (Whitney Reed, Dick Savitt), Great Britain (Bobby Wilson, Mike Sangster), Canada (Lorne Main, Henri Rochon, Don McCormick, Jim Boyce), Italy (Nicola Pietrangeli, Orlando Sirola), Sweden (Sven Davidson, Ulf Schmidt), France (Paul Remy, Pierre Darmon), Germany (Rupert Huber), Belgium (Jacques Brichant), Denmark (Kurt Nielsen, Torben Ulrich), Mexico (Mario Llamas, Rafael Osuna), Guatemala (Juan Jose Hermosilla), Cuba (Reynaldo Garrido), Brazil (Armando Vieira), Ecuador (Eduardo Zuleta), South Africa (Gordon Forbes, Bob Mark), Rhodesia (Adrian Bey), India (Ramanathan Krishnan), Viet Nam (Christian Duxin), Philippines (Willie Hernandez). Bédard defeated many World top ten players, of whom Savitt, Emerson, Osuna achieved World No. 1 ranking, Davidson achieved World No. 2, Quist, Pietrangeli, Krishnan achieved World No. 3, Nielsen, Bryan Grant achieved World No. 6, Sangster, Scott, and Holmberg achieved World No. 7, and Schmidt, Darmon, Mark, achieved World No. 8. Reed was ranked No. 1 in the U.S. and Straight Clark was ranked No. 5 in the U.S. College tennis player During the 1952–53 school year, Bédard attended UCLA on a tennis scholarship provided by his home community supporters in Sherbrooke, Quebec. This would be his only formal tennis coaching, and he was otherwise a self-taught player. During that same scholastic year, Bédard's fellow Canadian tennis player and later Davis Cup teammate Don Fontana was also in the UCLA tennis program on a tennis scholarship. Bédard and Fontana played against Bill Tilden and his student in possibly the final matches of Tilden's life, shortly before he died. Amateur 1952-1953 Bédard won the Montreal Cup in August 1952 beating Jack Spencer in the final. Bédard also won the Nova Scotia Championships that year. In 1953, Bédard reached the semi finals of the Quebec championships, also known as the Eastern Canadian Championships, losing in three straight sets to Lorne Main. 1954 Bédard