Elphin was both a Parish and a Townland in the Union of Strokestown, Castlerea, Roscommon and Athlone.

No place name Ballyglasson in Griffith Valuation 1857.

I thought there might be a Union of Elphin, but no.

I note in the phone book for Roscommon just 1 person with the surname Nolan living in Ballygar. I'm very surprised only one Nolan with a landline in Roscommon?

*see Civil Registrations below:
There are 15 McManus, many Murray's, 14 O'Connell's,
1 Dennigan, 18 Connor's.

I check Griffith but that name isn't listed, although perhaps it was a townland.

The 1911 Census shows 249 individual Nolan's but I think her parents would of barely been born by then.
Did she marry? if so what are her children's names they usually hold the clue to her parents names.

www.familysearch.org these could be possibilities:

Bridget J.Nolan birth registered *Roscommon July-Sept 1932
Mo: McManus LDS Vol.3 Pg. 165 #4195647

Bridget A.Nolan birth reg.April-June, *Roscommon
Mo: Dennigan LDS Vol. 3 Pg. 161 #4195648

Bridget F. Nolan birth reg. April-June,1928
Mo: O'Connell LDS Vol. 3, Pg. 184 #4195650

Bridget Monica Nolan birth reg. April-June 1927 *Athlone
Mo: none listed LDS Vol 3 Pg. 2 #4195645

Bridget M. Nolan birth reg. July-Sept 1934 *Boyle
Mo: Connor LDS Vol.4 Pg. 59 #4195647

Mary Bridget Nolan birth reg.Oct-Dec 1929 *Athlone
Mo: Murray LDS Vol.1 Pg. 9 #4195646

Note above that Roscommon was a Civil Registration District for Elphin.

I'm not sure if the microfilm would have the father's name
or not, I can't see this many women unmarried!! The earlier
microfilm often had no parents name and from 1864-1875 had
both parents names. Hopefully, your Bridget has a matching
middle name. You can expand the time frame to earlier or later.

There are other children with same mother's surnames as above so would probably be siblings (sibs usually 2 years apart)

Annette Code