Refers specifically to the chess piece. In Japanese chess contexts, the English loanword ビショップ is standard.
In chess, the bishop moves diagonally.
Refers to the Christian clerical rank. In Japanese, 司教 (しきょう) is the more common native term, but ビショップ is used in some contexts, especially when referring to Western churches or in translated materials.
The bishop of that church conducted Sunday Mass.