It's hard I know and as we have said Castlebar could mean a who area and I would still wonder re both Mayo - presumably they didn't enter place of birth in any other census.
Funnily enough I live in Oldham with Mayo family too- it was my dad though so later times than censuses.
Sorry to harp on about it but do the witnesses not give clues?
They signed with a X One was Patrick Smith and I can not read the other name, but there is no other details.
I have gone back to the 1841 Census looking up Patrick Costello (or near name) and there are two or three had daughters called Bridget, but not near her DOB. I have done thesame for Bridget, with father Patrick, but no luck.
So if they married ages 21 in Rotherham, why did they not marry in Ireland?, if they lived in England why do not any links come up on the 1861 census, and both fathers were dead by 1871, so I can not trace their family in England in 1871.
So both families could have left Ireland in/after1861, they must have lived in the rotherham area to marry there, and met in the mid 1860s and married in 1868.
The strange thing is, the witnesses did not have their names, so the families may not have come over from Ireland?. As they say "more questions than answers. !!!!
Do you live in Oldham, or Heywood? I worked there in the 60s.