In Belden, "Ballads and Songs Collected by the Missouri Folk-Lore Society," as noted by Gargoyle, the "Must I go (be) bound" verse appears in three of the four versions of the "The Blue-Eyed Boy that he collected in 1909-1911. None has the mantle or vinegar-gall lines. Two involve a girl who is going away and in one the boy departs, leaving "an orphant girl without a home."
In a footnote, Belden suggests the song goes back to the 17th c. (Roxburghe Ballads VII 104-5), but not which verse(s). he does say "divers images or motifs seem to have been gathered around a refrain stanza (Bring me back the blue-eyed boy) which gives the name to the song."

The song is not in "Folk Songs of Peggy Seeger," Oak, 1964