Whall 1927, has "Run, Let the Bulgine Run" on p. 139:

O a bulgine once was a heaving
O run, let the bulgine run.
Way, ah, o-o-o-oh, run, let the bulgine run.

O, New York town is a-burning, etc.

Whall says, "It had no set of [sic] words, but was popular. It is of a debased kind, and was quite unworthy of its popularity."

Whall's tune is about the same as those on the Carpenter CD.