Hi there:
There is a John Butler and Maria McInerney family who have several children born in the years mentioned in your post. Unfortunately, the Sixmilebridge (Kilfinaghta civil parish) baptism registers begin in 1828, so Bridget's baptism is probably too early for the register. If you would like to look at the transcriptions done, they are available on the Kilfinaghta civil parish page on the Clare Library website at this link: https://www.clarelibrary.ie/eolas/coclare/places/kilfinaghty.htm
The best of luck with your research. You are more than welcome to contact me via this thread if you have any further questions. Jane.