The 1891 census for Mary McIver Mooney, has any of the family viewed the original given Ancestry at least showed:
Elizabeth McIoor 50 Sister, Servant Domestic b. Ireland
If this was Bridget, at the very least she should show as sister in law not sister to Hugh (relationship is always given to head of household on the censuses).
I quoted a better transcription in Reply#8 yesterday, but I agree that you need to look at the original document.
Elizabeth McIvor, widow, sister, aged 50.
If she is Hugh Mooney's sister, then she isn't Bridget Kerr or McIvor, because Bridget Kerr or McIvor was Hugh Mooney's mother-in-law. And she is 22 years old than Hugh Mooney's wife Mary McIvor or Mooney, and (if the date of birth you have for Bridget Kerr or McIvor in 1837 is correct) only 3 years younger than Bridget Kerr or McIvor.
Given that the mother both of Mary McIvor or Mooney and of Catherine McIvor or Grenary is named as Bridget Kerr or McIvor on both their birth certificates and as Elizabeth Kerr or McIvor on both their marriage certificates and both their death certificates, we know that Bridget became Elizabeth at some point.
Is it too much of a leap to conclude that Elizabeth McIvor, aged 50 in 1891, is in fact Bridget Kerr or McIvor, who was 53 on census day 1891?