Had a quick look and BOL/TB became crossed with another song sometime in the 18th century (The Old Grey Mare, Roud 294/5418, ODNR 276). This song is equally as old as TB or perhaps even older. I've traced it back to 1559. It is the 3rd verse of your 1765 version above, still featuring in our local versions. In 'The Old Grey Mare' this stanza is usually the first one and the strong likelihood is it belonged to that song first. The song is actually scarce in collections but is quite widespread in England. The only American version I can see is in Our Singing Country p113 from Kentucky.