Hi Anne,
It's a little out of my area but did some digging and hopefully may have some possible leads and/or useful information.
I found an Ellen Kennedy who arrived in New York City, NY on July 7, 1901, by way of Liverpool, England. She is listed on both the "Arriving Passenger and Crew Lists" and "Record of Detained Alien Passengers" of the Campania. The text is hard to read in the detained passengers list, specifically the "Cause of Detention" section (possibly says "cous. E. Orange, N.J."), but listed in the "Disposition" section is "[cous.?], Mary Doyle, 61 S. Grove St., [Brick Church?], N.J.".
There is a Mary Doyle who was living at this address. According to the 1900 United States Census, this Mary Doyle immigrated to the U.S. in 1893 and is listed as a servant of the Jackson family headed by Francis Whiting Jackson (Mar. 20, 1841-Feb. 28, 1922). The Jacksons lived at the address from around 1893 to 1904, and Mary remained with the family at 125 Grove St., East Orange, NJ, until at least 1910 (per the 1910 U.S. Census). If this is the same Mary Doyle, it's unclear how long Ellen was employed and/or living at the 61 S. Grove St. address.
Do you have any more information on Mary? She was 44 and unmarried at the time of the 1910 U.S. Census. It's possible Ellen may be mentioned in Mary's obituary.
Presumably, Ellen married and settled in Bridgeport sometime after 1905? 590 E. Main Street was the address of the "White Mig [Mfg] Co." [The Coe & White Co.]. It apparently housed several employees, or they used it as a forwarding address, during the 1900s but I wasn't able to find an Ellen Kennedy or Ellen Cullinane among them.
The only "Cullinane" found in the Bridgeport, CT City Directory during that time period was a Mary Cullinane who was living at 352 Warren in 1908. There is an "Ellen E. Cullinan" listed in the Bridgeport, CT City Directory. However, she was the daughter John J. Cullinan (1864-1952) and Katherine Kennedy (1880-1960) who married in Naugatuck, CT on June 8, 1904 (Katherine was born in Naugatuck to John and Mary Kennedy).
The Cullinan family were fairly prominent in Bridgeport around the turn of the 20th century. Its patriarch, John Cullinan (1840-1924), a widely known funeral director-undertaker, was an Irish immigrant who arrived in Bridgeport around 1869. His sons, John J. (1864-1952) & Thomas M. Cullinan (1867-1928), founded the Cullinan & Cullinan law firm. Is there any chance Ellen's husband could be related?