We've had much discussion about the M.S. BLOEMFONTEIN on this forum - (scroll just a little further down).
It is likely that your dad joined her in San Francisco whilst she was undergoing conversion to a troopship (March/April 1942). He would have been part of her US Navy Armed Guard contingent and not part of her regular crew, which remained Dutch. The U.S. Navy Armed Guard was a service branch of the United States Navy that was responsible for defending U.S. and Allied merchant ships from attack by enemy aircraft, submarines and surface ships during World War II. The men of the Armed Guard served primarily as gunners, signal men and radio operators on cargo ships, tankers, troop ships and other merchant vessels.
BLOEMFONTEIN left San Francisco on 13 April 1942 on her 34th voyage, through the Panama Canal to Newport News VA. Your dad was probably then assigned to another ship, this being the S.S. PENNMAR bound for England. It was not uncommon for members of the US Navy Armed Guard to be reassigned to another vessel when the port of destination was reached or when circumstances required them elsewhere. There was no relationship between the BLOEMFONTEIN and the PENNMAR.
Home Port: New York, NY
Company: Calmar Steamship Corp. New York, NY
Master: Sigmond C. Krolikowski
Built: 1919 Kawasaki Dockyard Company Limited, Kobe, Japan
Dimensions: 385' x 51' x 26'
Gross Registered Tonnnage: 5868
Speed: 9 knots
Former Names: (a) EASTERN OCEAN (b) GEORGE ALLEN
Armament: 1 x 4”, 1 x 3’, 4 x 20mm, 4 x .50cal and 2 x .30cal
S.S. PENNMAR departed from Halifax, Nova Scotia with (slow) Convoy SC-100 on 12 September 1942 bound for Liverpool, England; laden with steel, food, trucks and general cargo. She straggled from the convoy due to steering gear problems. During early evening on September 23 in position 58°25N 32°15W, she was attacked by U-432 which fired a single torpedo at her. The torpedo was spotted and evaded after which her stern gun crew fired 4 x 4" rounds at the submarine. At 0144 on 24 September, the submarine again fired 4 torpedoes at her, of which one hit on the port side. The 8 officers, 31 crewmen and 22 Navy Armed Guard personnel abandoned ship in one lifeboat and two rafts while the ship was sinking rapidly; two crewmen dying in the process.
After spending 60 hours in the lifeboat and rafts, the survivors were picked up by the US Coast Guard Cutter BIBB (WPG 31) and taken to Reykjavik, arriving there on 2 October 1942.
Incidentally, five other ships from Convoy SC-100 were also sunk by U-Boats.
You asked: "Would the navy have shipped him back to the west coast for treatment because he was attached to the bloemfontein?" Well, you didn't say where he was from, but that he was hospitalised at Treasure Island, San Francisco on 30 November 1942. Naval Station Treasure Island was primarily a training school for electronics and radio communications at the time and it is my guess that he was not sent West for treatment but that he became sick or was injured while undergoing training. You do not indicate whether he again joined the BLOEMFONTEIN or any other ship. What do his records say - where did he go after leaving Treasure Island? And, what was his name?