Might not Ada Brice and Ada Hilson be the same person?
You said that Ada Brice's mother was a Hilson
Marriage, Sep 1892 Bedford 3b 628
Brice, Joseph
Hilson, Annie
According to the 1901 census, daughter Ada was born circa 1892, but there seems to be no birth registration
So the birth already mentioned in March qtr 1892 St Neots of Ada Eliza E Hilson might suggest that Ada was born before Annie Hilson married Joseph
There was an Ada Hillson born later in 1892 in St Neots district (coincidentally her father was called Joseph?) but that is Ada Alice Hilson who seems to have married in St Neots in 1914
So your Ada could have married using the name she was born with, Hilson, whilst naming her father (or he could have been a stepfather) as Joseph Brice. And there needn't have been any marriage for her as Ada Brice to a Mr Bird!
You could perhaps get the marriage of Ada Hilson to Leonard Bird in 1912, and see what she says on that one.
Is this her death?
March 1971 Bedford 4a 207
Robins, Ada Elizabeth
d-o-b 1 Dec 1891
John