Reprinted Scots books that contain song and tune are Scots Musical Museum, #164, and Orpheus Caledonius, (2nd ed.) II, 1733. John Glen's Early Scottish Melodies, p. 48, 1900 (recently reprinted) gives a copy of the tune from a late 17th century Scots MS. There are many other less readily available copies of the tune.

In you can use it, here's an early copy in ABC. X:1 T:B036- Bonny Katherine Ogie N:Simpson's BBBM from additional sheet of 7th ed. N:of The Dancing Master, c 1687. N:Also in Apollo's Banquet, 1687. Q:60 L:1/4 M:C| K:Bb G/2|DGG3/2A/2|BGG3/2c/2|c3/2d/2 (c/2A/2) (G/2F/2)|F3/2G/2A3/2 (G/4F/4)|DGG3/2A/2|BGGf|d c/2d/2 (f/2d/2) (c/2A/2)|G2 B3/2::A/2|(B/2c/2) (d/2e/2) (f/2e/2) (d/2c/2)|(B/2c/2) (d/2=e/2)f3/2c/2|Af(c/2A/2) (G/2F/2)|F3/2G/2A3/2(G/4A/4)| BGG3/2A/2|BGf3/2g/2|(a/2g/2) (f/2d/2) (c/2d/2) (c/2A/2)|G2 B3/2|]