"Lay the Bent (not Bairn!) to the Bonnie Broom" is a refrain that properly belongs to Riddles Wisely Expounded, as Sorcha says.  Pentangle recorded a set of Cruel Sister back in the 1970s, which used both the tune and refrain from RWE, and which has confused the issue ever since.  Frankie Armstrong did, too, and I suspect that she got it (the tune and refrain, that is), as they probably did, from Roy Harris.  Obviously, there are a great many references here to the song-family (Child #10); you might like to look at this one:

TWO SISTERS (Bonnie Broom)

It's quite close to the Pentangle set, but is probably -like theirs- a modern collation rather than an authentic traditional song.

Malcolm