Egan is spelled correctly the note about no Egan's buried there meant none of that name in the cemetary. The person who put the records out from the cemetary must of had a reason to comment, perhaps Egan's were part of her family.
Google the cemetary and you should see the record.
The Loftus fathers of Bridget are Thomas, Patrick Michael and John, only a couple of unusual ones. Again the difficulty of such common names.
From LDS, CD (www.familysearch.org
I did find something after all, using ALL Ireland instead of a county and both parents names:
Daniel Egan & Margaret Shannahan
Bridget Egan registered birth 6 Apr 1870 #286 Miltown Malbay,CLARE LDS#101213
Catherine Egan reg.birth 19 Nov 1871 #269 Miltown Malboy, Clare LDS#255836
Michael Egan reg: birth 21 Sept 1873, MiltownMalbay,Clare
John Nary reg. birth 3 Oct 1872, Castleconnor, Sligo
fa: Patt Nary/mo: Bridget Loftus LDS#355864
You can get certified copies of these from the General Registry Office in Dublin www.groireland.ie
With both parents names you should be able to get all the children born to this couple.