2009-10: Antoine Bibeau played in Quebec midget AAA hockey as a 15-year-old, playing for the Trois-Rivieres Estacades. Sharing the goaltending duties with Jimmy Appleby, he was 8-4, appearing in 22 games, and had a 3.46 goals against and .864 save percentage. In two playoff games he was 0-1 with a 7.55 goals against and .761 save percentage. Bilbeau was selected by Lewiston in the fifth round (73rd overall) of the 2010 QMJHL Entry Draft.
2010-11: Bibeau made his QMJHL debut, appearing in three games for Lewiston, and returned to Trois-Rivieres for a second season. In his time with the MAINEiacs, one of the QMJHL's top teams, he was 2-0 with a 2.10 goals against and .914 save percentage. In 29 regular season games for Trois-Rivieres he was 16-8 and had a 3.27 goals against and .895 save percentage. In five playoff games he was 2-3 with a 4.74 goals against and .837 save percentage.
2011-12: Bibeau played for the Prince Edward Island Rocket after being obtained in a pre-season trade with Gatineau, which had selected him in the QMJHL Dispersal Draft after Lewiston folded. Playing behind returning goalie Maxime Lagace, he played 29 games and was 7-9-1 with a 4.46 goals against and .868 save percentage. Prince Edward Island missed the QMJHL playoffs; finishing last in the Maritimes Division.
2012-13: Bibeau emerged as the starter for Prince Edward Island ahead of Lagace in his second QMJHL season, appearing in 46 games as the Rocket moved up to third in the Maritimes Division. Bibeau was 28-11-3 with five shutouts and had a 2.81 goals against and .911 save percentage. In six playoff games Bibeau was 2-4, with one loss coming in overtime, and had a 3.37 save percentage and .907 save percentage. Bibeau, who was not listed in Central Scouting's mid-season rankings, was ranked ninth among North American goalies in their final rankings prior to the 2013 NHL Draft.