In the James Madison Carpenter collection at the Library of Congress we have a version collected from Edward Robinson:

John Brown's body in the alley
So help my Bob, I'm bully in the alley
Bully in Shinbone Alley
Away, hey! Bully in the alley

I lost my jacket in the alley
So help my Bob, I'm bully in the alley
Bully in Shinbone Alley
Away, hey! Bully in the alley

And one collected from James Forman of Leith:

O, I lost my coat in Storrie's Alley
O-o-o I'm bully in the alley!
He chucked me out because I had no money
Way-ay-ay, I'm bully in the alley

Mary Jane is my good fancy
O-o-o I'm bully in the alley!
But she took my watch and stole my money
Way-ay-ay, I'm bully in the alley

She pawned my clothes in Storrie's Alley
O-o-o I'm bully in the alley!
And then she kicked me out me out because I had no money
Way-ay-ay, I'm bully in the alley

I'll see what else i can turn up about these versions....