This shanty is clearly of African-American origin.
Bullgine is American slang for engine, as seen in Clear the Track. Laura Alexandrine Smith, British author of the 1888 collection The Music of the Water, seems to have misheard "Let the Bull Chimes Run". She gives no explanation to this "favourite pumping song".
The Great Australian Bight, in Runciman's variant, is the large open bay to the southwest of the continent.