Bibeau was selected by the Toronto Maple Leafs in the sixth round (No. 172) in the 2013 NHL Draft after he went 28-11-3 with a 2.81 goals-against average and .911 save percentage for P.E.I. in the Quebec Major Junior Hockey League.
In 2013-14 with Val d'Or of the QMJHL, Bibeau won the Guy Lafleur Trophy as the playoffs most valuable player after he went 16-8 with a 2.80 GAA, .913 save percentage and one shutout in 24 games to help it win the President's Cup. Val d'Or also played in the 2014 Memorial Cup, and Bibeau was named to the Memorial Cup's most outstanding goaltender.