In a separate thread, I will post "Wake Up, Jake- Old Iron City," by George Holman, also about the bulgine, given the date 1848 by Levy, but the sheet music they show should have the date 1850. The song ("Sable Harmonists') is printed with "Susanna," printed also by Peters in the same folio. It may be contemporaneous with Foster's "Susanna." The 'Iron City' is Pittsburgh, but Cincinnati also claimed the song in according to an online article.

The most famous locomotive in America is the John Bull, the name given to the English-built engine first used on the Cambden & Amboy RR in New Jersey in 1831 (service 1833-1866), and featured at exhibitions in 1876, etc. At the Smithsonian since 1884, it was last fired up in 1881. A replica was built for the Railroad Museum of Pennsylvania.
This locomotive also could have been the source of 'bulgine.'

Further online sources show that the term 'bulgine was in common usage, appearing in reports of the westward expansion of the railroads.
Lighter points out some early uses, here are a couple more to fill out.

Wm. W. H. Davis, 1887?, "History of the Doylestown Guards," - "The 1st Pennsylvania Regiment, Colonel Yoke, and the Batallion of the 25th took the same train with bag and baggage; steam was turned on the "bulgine," the band played "Home, Sweet Home," ...

NY Times, Dec. 3, 1893, "Middies again triumphant- West Point Cadets whipped at football by two points." Bulgine used as part of a yell encouraging their players- "Bulgine! Eushline! Reeves! etc."

W. O. Payne, "History of Story County, Iowa; ..." The bulgine comes to town, Marshalltown reached in 1864, etc.. (bad transcription).

George Lippard, 1850, "The Killers...," a novel about New York, and "New York: Its Upper Ten and Lower Million," bulgines mentioned.

Adding to Rudyard Kipling usage, the Kipling Society website notes that Kipling's language was toned down for publication; the "blighted bulgine" changed to "running Bulgine." See his "Steam Tactics" and "Traffics and Discoveries."

Several other uses in novels, political writings, etc. (one about Horace Rosinante Greeley in dialect, interesting- archive.org.

Blackface minstrel or railroad worker still seem the most likely sources for the word's origin. No evidence found of prior slave or free Black usage.