Your could try Ellis Island. Many came through this port in NY. Here is the link. It is free to search and register.
http://www.ellisisland.orgDo you know Beatrice's age? It will help in the search. There is someone in 1903 who looks promising if you knew her DOB.
First Name: Beatrice
Last Name: Turner
Ethnicity: England, English
Last Place of Residence: Malvern
Date of Arrival: October 31, 1903
Age at Arrival: 36y Gender: F Marital Status: M
Ship of Travel: Etruria
Port of Departure: Liverpool
Manifest Line Number: 0023
Any way, happy searching. Kristin