Why don't you get Bernice Arthur's immigration records. I checked the Ellis Island site and got this information. She arrived at Ellis Island and you can get the ship manifest for a price.

Bernice Arthur, British African
Residence: St Thomas Barbados
Arrival: September 26, 1923
Age 29 years old
Marital Status: Single
Ship: FRANCIS
Port of Departure: Bridgetown, Saint Michael, Barbados.