a complicated word of uncertain history. First attested late 15c., "lewd person" (of either sex; since c.1700 applied only to women), probably from baude-strote "procurer of prostitutes" (mid-14c.), which may be from Middle English bawde (adj.) "merry, joyous," from Old French baud "gay, licentious" (from Frankish bald "bold" or some such Germanic source). It would not be the first time a word meaning "joyous" had taken on a sexual sense. The sense evolution shading from "bold" to "lewd" is not difficult; cf. Old French baudise "ardor, joy, elation, act of boldness, presumption;" baudie "elation, high spirits," fole baudie "bawdry, shamelessness." The Old French word also is the source of French baudet "donkey," in Picardy dialect "loose woman."
The second element in baude-strote would be trot "one who runs errands," or Germanic *strutt (see strut). But OED doubts all this. There was an Old French baudestrote, baudetrot of the same meaning (13c.), and this may be the direct source of Middle English baude-strote. The obsolete word bronstrops "procuress," frequently found in Middleton's comedies, probably is an alteration of baude-strote.