Hmmm. Can't find much. The University of Tennessee - Knoxville Song Index says it's in an anthology called "Old Songs and Singing Games," which I don't have. Another book to check would be The Singing Game, by Iona and Peter Opie (don't have that, either). Maybe somebody here who has those books will check them for you.
However, I did find a brief entry in a book called Games and Songs of American Children (William Wells Newell, 1883 & 1903):

Four girls cross hands, and pull in a rhythmical movement against each other while singing, one pair changing the position of their hands from above to below that of the other pair at the words, "Here we go under," etc.

Draw a bucket of water
For my lady's daughter
One in a rush
Two in a rush
Here we go under the mulberry bush.
(this is how it was played in New York)

In Massachusetts, this was a ring game:

Draw a pail of water
For my lady's daughter
Give her a ring and a silver pin,
And pay for my lady's pop under.

At the last words, the girl within the ring endeavors to pass under the hands of one of the couples.

JRO