Aggie, you have an excellent voice for these things and I think you'd perform well, too. There are a huge number of books & many of them with tunes. I agree, though that this is a last resort and often fails to give the subtilties or even meaning of the song.
I'm sure you know, or you wouldn't have asked that bawdy song is extremely rare on record. What there is is very hard to find. I think the great bulk of recorded bawdy sources are from the blues area, though.
My own treasure is MacColl singing a good bunch from Burns' 'Merry Muses of Caledonia.' Often you are going to make a choice of how bawdy to sing of several versions - all the way from "parlor version" up to "keep the smelling salts handy" version. I've had some success in listening to Medium versions on record (eg Brand from his 'Bawdy Songs & Backroom Ballads' series or McCurdy from 'When Dalliance Was in Flower' series and then substituting in the set of words I want. Many known trad bawdy songs simply have never been recorded - Haywire Mac McClintock flat refused to record his, etc.
I have a feeling that you are more (or at least equally) interested on what you might call risque or suggestive types rather than all-out x-rated. These would likely go over better in public, anyway. (No dis, though. Did you want the words to "Charlotte the Harlot?") Look to the English records. As suggested, a DT search on @bawdy will yield many titles and many mainstream singers will do one or two on a typical record. Carthy, eg, sings "German Musicianer" & Bellamy sings "Yarmouth Town" (sort of same as Carthy's "Domeama") Cliff Haslem (& in a version, Elsa Lancaster) sings "The Old German Clockwinder." These are all fairly widely sung excellent songs.
There are quite a few excellent songs of this type. But, I think, they are not much recorded as specifically bawdry - more likely as just some typical material in a general folk selection. That's my own preference, BTW, neither exclusive nor excluded - just the normally proportional part of the known body of material. But I agree that a "wench" must sing bawdy (and other love) songs.
One book you might make an effort to get: The Wanton Seed. Also Marrow Bones from E.F.D.S. and if you want the extreme, then Silverman's The Dirty Song Book.
Sing ye well.