The song is pretty old. There are plenty of 18thc printings in garlands etc. The earliest I have seen is printed at Aldermary Churchyard by the Dicey-Marshall dynasty, so probably about mid century. Even in stall copies the titles vary Band, Bond, Bann, Bawn.
The 'Molly Bawn' intro line at the top of this thread is misleading. Ooops! I meant to remove the Molly Bawn reference. I did now. -Joe Offer-