The Bow down refrain was first (?) noted in England in the mid-19th century, and seems to have originated there, though at what time is unknown. Bronson (The Ballad as Song, 1969) cites a copy from Kent of c.1770, which contains the lines
Hay down down derry down
And the bough it was bent to me
I'll prove true to my love
If my love will prove true to me.
as an earlier form from which it may have developed. He considers the Bow down/ Bow and balance to me refrain to have developed in Appalachia as part of the "play party" tradition.
I put a rather long list of links to material relating to the Child #10 family of songs in this earlier thread:
'twasisters' lay the bent to bonny broom