late 14c., baudi, "soiled, dirty, filthy," from bawd + -y (2). Perhaps influenced by Middle English bauded, bowdet "soiled, dirty," from Welsh bawaidd "dirty," from baw "dirt, filth." Meaning "lewd, obscene, unchaste" is from 1510s, from notion of "pertaining to or befitting a bawd;" usually of language (originally to talk bawdy).
Bawdy Basket, the twenty-third rank of canters, who carry pins, tape, ballads and obscene books to sell. [Grose, "Dictionary of the Vulgar Tongue," 1785]
Related: Bawdily; bawdiness. Bawdy-house "house of prostitution" is from 1550s.