I also want to note that "Blue Bells/Cockle Shells" probably came from the nursery rhyme:

Mary, Mary, quite contrary,
How does your garden grow?
With silver bells, and cockle shells,
And pretty maids all in a row.

-snip-

It seems to me that the "easy ivy over" line is {or at least used to be} a movement instructional phrase that was associated with jumping. As such, I believe that the rhyme-if not the actual movements and the tune-is similar to elastic rhymes such as:

england
ireland
scotland
wales
inside outside inside on

{see thread.cfm?threadid=46932&messages=103#2345619; Girl's Games: Elastics}

**

Comparative Studies in Bursery Rhymes {Lina Eckenstein; Detroit, Michigan, Singing Tree Press, 1968; originally published London, Duckworth & Co, 1906}, is an excellent book on the origins of English language nursery rhymes. That author indicates that many nursery rhymes use tunes from non-religious popular songs as well as religious chants such as "Green Grow The Rushes, Oh".

Perhaps we'll never know the source of the tune for "Blue Bells, Cockle Shells" {which probably comes from "Mary Mary Quite Contrary". DMcG, I'm not sure if you were looking for the "original source" for this song or what you were looking for is the musical notes that are used for this rhyme/song. I'm interested in information about either or both.