A set of words, with the title "Bobby Shafto" (cross-referenced to another set called "Coulter's Candy") appears in the DT, but without music. Perhaps this is the tune.

X: 1
T: Bobby Shaftoe
C: 19th c. Northumbrian, from John Stokoe, ed., Northumbrian Minstrelsy (pipe), Newcastle-upon-Tyne, 1882, p. 35
M: 2/4
L: 1/8
K: G
|: c2 ed/c/ | gc e2 | dB/c/ dB | gB d2 | c2 ed/c/ | gc e2 | f/e/d/c/ B/c/d/B/ | c2 G2 :|
|: e/f/g ec | e/f/g e2 | dgdB | dg d2 | e/f/g/f/ e/f/g/f/ | e/f/g/f/ ec | f/e/d/c/ B/c/d/B/ | c2 G2 :|