I have some volumes of Bagford but it's not in any of the ones I've got. There are plenty of 17thc versions at UCSB EBBA site so it's worth having a look at all the versions there to see if any relate to a known tune.

If you want my opinion, this is highly unlikely. Jack says 'sometimes they printed that tune'. Whilst a small number did, the majority of these had no relation to the ballad whatsoever and were just there for cosmetic appearances.

Regarding Chappell's tune, it's quite probable that the ballad was still being sung in polite circles in Chappell's youth and that might have been a source of his tune. Chappell also lived in Edinburgh for much of his life so again it may well be a Scottish tune. His family business was based in London so a look into his life story might give a better picture. Wikipedia?