It's from the chorus of "A-Rollin' Down the River' as printed in Stan Hugill's "Shanties from the Seven Seas':

Oh, a pumpkin pudden an a bulgine pie,
A pumpkin pudden an' a bulgine pie,
A pumpkin pudden an' a bulgine pie,
Aboard the Arabella!

He explains "bulgine" as American slang name for a railway engine but doesn't explain the bulgine pie.