It may be that Mary Bridget was planning a trip to Ireland and wrote home to see who may still be living in the area and to get a passport looked for her birth certificate
I'ms not sure why she would be adopted as her parents married in 1892
John CULLEN a Baker & Mary Anne SHERIDAN a Dressmaker
They had five children
1 James Michael Joseph CULLEN b. Jun 21 1894
LINK2 Michael Francis CULLIN b. Apr 15 1898
LINK d. Dublin Aug 13 1899
LINK3 John Joseph CULLEN b. Jan 15 1900
LINK here John CULLEN Snr is shown as a Soldier
4 Mary Bridget CULLEN b. May 09 or 15 1903
5 Angela b. Sep 28 1910
LINKIn 1901 Mary is shown with her two sons in Wexford
LINKI cannot see John CULLEN Snr on the 1901 census
In 1911 Mary is shown with two children but states she ahd five of which four were alive
LINKJohn CULLEN Snr is in Dublin -
LINKThere are a few options for a James CULLEN bc1894 in Wexford on the 1911 census
but there is nothing very obviously for May Bridget although she may have been in hospital as her initials or elsewhere and omitted or incorrectly returned
There is nothing immediately jumping out that would imply she was adopted.
The fact she was not at home in 1911 aged 8 could mean she was with a grandparent or other relative with whom she continued to live. This was not unusual.