This song was quite popular aboard early 1800s packet ships. Liza Lee is the name of another tune of unrelated melody.
Captain Whall, Sea Songs and Shanties, traces this song to a minstrel ditty with chorus:
Walkee up, O walkee up, O walkee up, O way
Walk into de parlor for to hear de banjo play!
but other authors have suggested the melody and the phrase "low-back" jaunting car support an origin in the Irish folk-song "Shule Agra." One plausible explanation for this cross-cultural origin is based around New Orleans and other Gulf ports: black and Creole stevedores may have heard some Irish seamen humming Irish ditties. The cargo-loaders' wording would then have been added to supplement the cotton pressing work, and visiting seamen apparently took the songs for use at capstan and halyards.
The Margaret Evans was a well-known American packet-ship built in 1846 by Westervelt & MacKay. She sailed in and out of Liverpool, London, and New York, apparently for Grinnell, Minturn & Co.'s Swallowtail Line and before making her way to Griswold's Black "X" Line. Stan Hugill's version offers instead the Wild Cat of the Swallowtail line.
"Bullgine" was American slang for steam engine.