Bishop, who was eligible to become an unrestricted free agent this summer, signed a two-year, two-way contract with Calgary on Wednesday.
Bishop will carry a $775,000 cap hit if he plays in the NHL in 2023-24. The 27-year-old had 11 goals and 23 points in 64 contests with AHL Calgary in 2022-23. In 47 career NHL outings, he's contributed a goal and eight points.