It is based (verry loosely) on a version of Child #1. I've only read the version with Jennifer, etc. , so I can't point you to a performer or tune. Jean Redpath (among others) does a lovely job with a version called "Lay the Bent to the Bonney Broom" which has the supernatural riddler contending with three (unnamed) sisters, rather than a schoolboy, only one lady, etc.
Pamela Dean really disappointed me with this book. I kept slogging through, hoping to find something more than a tenuous connecion to the ballad. Her treatment of Tam Lin (same title for the book) was better. I liked other books in the Faery Tale series, though.