I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are sparse, B4 1800 rare. I only search the 65% which are.
For Bridget Rodgers M 1854 (exact) in Cavan, I found 1 M rcd. It is in the parish of Knockbride. It is highly likely to be for your ancestor. However, I can't find a matching M rcd for her spouse. Perhaps the surname was mangled when they transcribed it. But, if you view HER detailed rcd, it USUALLY shows the parents' names. It MAY also give her age.
There is a B rcd for Knockbride for a Bridget Rogers (a common mistake) in 1836. This has a fair chance of being for your ancestor.
Google the Foundation's name to lead you to the database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.