The records for Ballinasloe RC parish start in September 1820 and are available on the subscription site Roots Ireland. I searched for Bridget's baptismal record and did not:find a record. I also looked at the Co. Roscommon records since Ballinasloe is right on the border but no success there either.
I looked at the 1856 Griffiths Valuation head of household reocrds for Kilcloony civil parish which includes Ballinasloe and there were two Hoary records: John and Patrick who lived in the town. https://www.failteromhat.com/griffiths/galway/kilcloony.htm Not sure how they may be connected to Thomas.