SS Siboney, from Havana, Cuba, 24 Jun. 1922 to New York
Gillick, Rose, age 31, single, nurse, nationality - Gt. Britain, last permanent residence - USA (there's something written over that which looks like "Claim 2 yrs in California"?), nearest relative in country from whence she came - friend Louise Williams, 98 Prado Street, Havana, final destination - N.Y., N.Y., previously in US from 1920/22, going to 16 Exchange Place, New York, 5'8" tall, fair complexion, blond hair, blue eyes, born Oradook?, S. Australia
There are manifest markings on there that indicate that she later sought to be naturalized. She seems to show up on one of the naturalization indexes on italiangen.org, so that seems to fit.
SS Virginia, from New York 11 Jan. 1936 to California, 25 Jan. 1936
Gillick, Rose, age 45, female, single, nurse, nationality - British, race - Irish, born Adelaide, Australia, last permanent residence - New York, USA, nearest relative - brother James - Wirreganda, Craddock, Australia, final destination - New York, NY, previously in US from 1920-1936 in N.Y., going to join employer - Prof. W. Bush, 1220 Park Ave., N.Y. N.Y., 5'8" tall, fair complexion, brown hair, brown eyes
There are also some passenger lists for a Rose Dorothy Gillick, who seems to be about 5 years older, but the other information seems to fit and it seems to match the person in the Southern District Index on italiangen.org. Maybe she aged herself by 5 years?
SS Lafayette from Le Havre, France 25 Sep. 1935 to New York
Gillick, Rose D. - under her age, it looks like 44 was typed in, that was crossed out and 48 was written in and then crossed out and then 49 was written in. Otherwise, she was single, a nurse, nationality - British, race - English, born Adelaide, Australia, last permanent residence - N.Y. City, no relative in country from whence she came - stayed in hotel in Paris, France, final destination - N.Y. City, previously in US from 1934-1935 in NYC, last departure - 5/29, home - 1220 Park Ave., New York, NY (something written above about Mr. Prof. Bush), 5'7" tall, fair complexion, black hair, blue eyes
Record of Aliens held for special inquiry - SS Lafayette arrived 4 Oct. 1935
Gillick, Rose, cause of detention - not in poss. of proper I.V., given dinner, paroled by (someone) 10/4/35 3:00 p
SS Empress of Canada from Kobe, Japan 8 Sep. 1937 to Victoria, British Columbia 22 Sep. 1937 - List of US Citizens
Gillick, Rose Dorothy, age 50, female, single, born Sept. 29(?) 1886, So. Australia, naturalized by Department of Naturalization, New York City, Jan. 11, 1937, address in US - 1220 Park Ave., New York City
Right above her is a Wendell T. Bush, age 70, born Sept. 25, 1866 in Ridgeway, Michigan, with the same home address at 1220 Park Ave. Perhaps she was a private nurse & traveling with her employer?