There are other versions in the Forum, mostly with the Cutty Wren songs, but the relationship to that group is not clear-cut. Here is a "Billy Barlow" that was popular in Texas.

HUNTING THE WREN (BILLY BARLOW)

"Let's go hunting," said Rob-sha-Bob;
"Let's go hunting," said Ridge to Rodge;
"Let's go hunting," said Daniel Joe;
"Let's go hunting," said Billy Barlow.

"What shall we hunt?" said Rob-sha-Bob;
"What shall we hunt?" said Ridge to Rudge;
Etc.

"Go hunt a wren," said Rob-sha-Bob;
etc.

"How'll we kill it?" said Rob-sha-Bob:
etc.

"Go borrow a gun," said Rob-sha-Bob;
etc.

"How'll we cook it?" said Rob-sha-Bob;
etc.

"Go borrow a skillet," said Rob-sha-Bob;
etc.

"How'll we divide it?" said Rob-sha-Bob;
etc.

I'll take the head," said Rob-sha-Bob;
"I'll take the back," said Ridge to Rodge;
"I'll take the breast," said Daniel Joe;
"I'll take the rest," said Billy Barlow.

William A. Owens, 1950, "Texas Folk Songs," pp. 252-254, with music.