Birth records are on line, with both the parents names you should be able to find all the siblings on an Irish
History Foundation website. It is a pay website like most of ireland's genealogy. www.rootsireland.ie
From 1864-1950 you can find civil records for birth, marriage and deaths on www.familysearch.org
Don't be surprised by the name changed, it was quite common as families called their children basically all the same names and possibily Delia was what we now call a 'nickname'.
Its a stretch from Delia to Bedelia but I've seen some
really odd choices.www.familysearch.org
Bridget O'Connor birth registered birth March 4, 1876
fa: Patrick O'Connor Mo: Mary Haly
LDS, micro film #C00594-6/255945www.census.nationalarchives.ie
1901/1911 There are 41 Patrick OConnors in Sligo, Bridget's 21, Mary's 52.
Good luck with that. Match up Patrick & Mary's for a common address, the DED is Dedicated Electoral District yet again