Gibb-

Naturally, there are plenty of words and idioms that are in general use now but that were once used mainly by a certain group. I see no evidence that "bullgine/bulgine" was "general use" during the period 1840s-50s in which these chanteys were most likely conceived.

Given that a popular novel was in fact using the term "bulgine" in 1853 as citied above, would you consider revising your opinion:

New York: Its Upper Ten and Lower Million
by George Lippard, published by Queen City Publishing House,
© 1853, p. 105

Lacking a time machine, Google does provide alternative access!

Cheerily,
Charley Noble