I've been slowly working my way through the Folktrax double CD of Shanties from the James M Carpenter Collection (housed in the Library of Congress, Washington DC), and came across a couple of interesting versions of Run, Let the Bulgine Run which mention New York being on fire.
The recording quality is extremely poor, and many words are indecipherable. Only a portion of the song was recorded anyway. The main collection is not online, but the Carpenter Collection Catalogue has been digitised and gives a bit more information about text versions and some details of the singer.
Here are my transcriptions of the two versions:

---

Run, Let The Bulgine, Run
(Jack Murray, Aberdeen. Born 1854. Went to sea in 1867, learned chanties between 1867 and 1885. In the ship Zedring, St John's New Brunswick, 1874 or 1875, a Canadian ship. On board the Luke Simcoe, 47 years ago [c. 1883]. In the Star of Dundee, a whaler, 45 years ago [c. 1885]) 3 stanzas in text but only 2 on recording.

Oh New York was on fire
Oh run, let the Bulgine run.
Way-hay, o-oh-oh
Oh, run, let the Bulgine run.

For New York was [in blazes?]
Oh run, let the Bulgine run.
Way-hay-o-oh oh
Oh, run, let the Bulgine run.

---

Run With The Bulgine, Run
(James Forman, Leith. born 1844. First ship 1856; second 1900 ) 4 stanzas in text but only 3 on recording.

Oh [airlock?] fire [blow over?]
Run with the Bulgine run.
Way-hey, o-oh-oh
Run, let the Bulgine run.

London docks is on fire
Run, let the Bulgine run.
Way-ah, o-oh Joe
Oh, run, let the Bulgine run.

Oh, New York city's in the fire
Run, with the Bulgine run.
Way-ah, o-oh-oh
Run, let the Bulgine run.

---

The online catalogue also mentions other texts and recordings with no apparent fire content:
Run with the Bulgine [song text] First line: Run with the bulgine. Fragment. James Dwyer, Glasgow.
Run Let the Bulgine Run [song text] First line The bulgine's come and we all must go-o. 6 stanzas. William Fender, Barry. Sailed in ship Ingomar, 1880, Valparaiso, Chile. Went to sea 1878; left sail 1900.
Run Let the Bulgine Run[song text] First line The bulgine's come and we all must go. 2 stanzas. William Fender (as above).
Run Let Bulgine Run [sound recording], Barry Docks. (Presumably W Fender?)
Hugill has versions of this shanty, but none referring to a fire in NYC, and I haven't found any more through Google.

Does anybody :

• know of any other versions referring to a New York fire, or
  
• know any details of the fire it refers to, or
  
• have access to the song texts in the LoC, or
  
• know more verses of this.
  

BTW in these versions it appears the "bulgine" could be used for firefighting duties, presumably for pumping water onto the fire. But was it on board or on shore?

WassaiL! V