The story
Uncertain or disputed. Goldman (1950) suggests that beat the bishop comes from a resemblance of the penis to a bishop’s miter; Partridge (7th ed., 1970) likewise derives bash the bishop from a resemblance to the Staunton bishop chess piece. Other sources, such as Green, suggest that assonance of bishop with bash, beat, bop etc. may have given rise to the phrase as a type of word play.
Etymology from Wiktionary, CC BY-SA 4.0.