From the book (and there's more): The General Lyon, commanded by Captain Minott Ward, sailed from New York harbor on March 16th, 1865 bound for Wilmington via Fortress Monroe. She was carrying 554 recruits for delivery to Union armies in Virginia and North Carolina. The men had departed from Camp Rendezvous on Hart Island, escorted by twenty-two enlisted men of the Permanent Party, Companies C and D, under the command of Captain James Bullock (20 years of age), Fifteenth New Jersey Volunteers. Bullock’s second in command was Lt. Edgar Simpkins (27) of Company B, One Hundred Twentieth New York Volunteer Infantry.

If you haven't found it already, Google "UNCOUNTED COSTS: THE CIVIL WAR’S IMPACT ON AN INFANTRY COMPANY’S MEN AND THEIR FAMILIES" a dissertation by Michael Heaney at Rutgers has much about James Bullock. His speculation about why Bullock was on board and the destination is not quite accurate. But his career is well covered and that of his friend Paul Kuhl

Also: HISTORY OF THE Fifteenth Regiment of JERSEY VOLUNTEERS.
ALANSON A. HAINES, Chaplain of the Regiment.
NEW YORK: Jenkins & Thomas, Printers, No. 8 Spruce St 1883

"Intelligence reached us of the death of Captain James L Bullock, by burning of the' Steamer General Lyon, at sea off Cape Hatteras. A most worthy and excellent young man, of decided talent, he had been detailed on recruiting service, and was in command of a large number of recruits, who were being forwarded to regiments in the South"

https://openlibrary.org/books/OL6917169M/History_of_the_Fifteenth_Regiment_New_Jersey_Volunteers.

On my Facebook page "Steamship General Lyon - Going Home", I just added a photo from the NARA CMSR of Hobart Walker; Extract from Hart Island Records; Johnson, Asst. Adjutant General. It mentions Bullock

Also see the New York Herald, April 04, 1865; letter from Captain and A. A. Inspector General, George E. Trembley; names of officers and enlisted men lost on the General Lyon

Good luck with your research