Jon,
There are 2 versions in Sandberg's American Songbag. The version sung by Burl Ives appears to be the first one on p14. The other is at p.460. He got the first version from Arthur Sutherland and his Bold Buccaneers at the Eclectic Club of Wesleyan University. A middle verse was censored as 'being out of key and probably an interpolation'. Both versions have the same 2 stanzas 'When I was a bachelor' and 'Oh I am a bachelor and I live with my son' so the omitted verse was probably the 'jumped into bed' stanza.

I would guess that this version was probably part of the student repertoire along with pieces like 'My Bonny' and 'Landlord fill the Flowing Bowl' in the 1880s.