I've known "Bill Bailey won't you please come home" from childhood and have heard it performed by many jazz groups in England and Germany. Not so long ago (1998) I had the chance of singing this number with a local jazz group, friends of Peter Krüger, but my performance wasn't very successful, sadly. I just couldn't get on with the microphones and amplifiers. Jazz singing is quite different from singing folk music.
The lyrics are rather rare in that the narrator, a lady, admits that she has done wrong, and is even prepared to do the cooking and pay the rent to keep her Bill. Al Bundy would love it!. The version I sing can be found in 101 Pub Favourites for Buskers