Bear was born in Regina, Saskatchewan and raised in the Ochapowace Nation near Whitewood, Saskatchewan and drew inspiration from his brother Everett and other Indigenous hockey players including Carey Price, Jordin Tootoo, Brandon Montour, Arron Asham and Micheal Ferland.
Bear was chosen by the Edmonton Oilers in the fifth round (No. 124) of the 2015 NHL Draft. He played four seasons for Seattle of the Western Hockey League and signed a three-year, entry-level contract with the Oilers on July 2, 2016. He made his NHL debut against the Nashville Predators on March 1, 2018 and scored his first NHL goal in a 5-4 overtime loss to the Anaheim Ducks on March 25.