Had a look at potential illegitimate births for BULLOCK from 1893 (when Mary E BULLOCK was 18) until 1899 (when she married Peter NASH) and only found 2 births GRO registered in Chepstow:
Charlie BULLOCK born 1893 Q1 Chepstow v11a p13 GlosBMD FOD Lydney 22 182
Constance Ailine Johnson BULLOCK born 1896 Q3 v11a p12 GlosBMD Lydney 24 50

However Charlie BULLOCK born 1893 died in 1916. Constance Ailine Johnson BULLOCK not recorded as a death, therefore survived and married. This means that neither of these are one of the pre 1911 births died by 1911 in the 1911 census in my original question.

Mary Elizabeth BULLOCK was born in 1875 in the Forest Of Dean: GRO Q4 Monmouth v11a p25 no mother’s name, GlosBMD Forest of Dean Coleford 33 84, indicating that she was illegitimate. No baptism on FoD, Ancestry or Findmypast. A pdf copy of birth certificate ordered to identify her mother.

There are no illegitimate Bullock births registered at Monmouth 1893-99.

Looking further afield:

Westbury-on-Severn
1) Annie Elsie BULLOCK born 1893 GRO Westbury on Severn v6a p243 Glos BMD FOD Newnham 1 87
2) George BULLOCK born 1894 GRO Westbury v6a p227 GlosBMD FOD Newnham 1 263 (GlosBMD says from 1893, does this mean late reporting in 1894 of a birth in 1893?)
3) Ernest BULLOCK born 1895 GRO Westbury v6a 249 GlosBMD FOD Newnham 1 384 (from 1893). He died 1896 Q1 Westbury v6a p149 aged 0 GlosBMD Newnham 1 328 aged 7mo. There are baptism and burial on FoD. Baptism 16.6.1895 at Westbury by Leonard Wilkinson, vicar with the note ‘a bastard child’ and mother's name Edith, a single woman. This therefore excludes him. Burial 30.1.1896 at 7mo at Westbury by Leonard Wilkinson, vicar.
4) Harry BULLOCK born 1896 GRO Westbury v6a p234 GlosBMD FOD Newnham 1 17 (from 1893)
5) Edith Mary BULLOCK born 1897 GRO Westbury v6a p242 GlosBMD FOD East Dean 5 428
6) John BULLOCK born 1899 GRO Westbury v6a p303 GlosBMD FOD Newnham 3 28 (from 1893)

The others died later, or the girls must have married as not recorded as a death in single name.

Bridgend - perhaps this is where she was living before she married Peter Nash in Bridgend in 1899
Margaret Ann BULLOCK born 1894 Q1 Bridgend v11a 824, and died in 1894 Q1 Bridgend v11a p441 aged 0. No baptism to identify her mother. A pdf copy of birth certificate ordered to identify her mother.

By process of elimination, the only illegitimate BULLOCK birth that seems to fit the bill is Margaret Ann BULLOCK b1894 d1894, so would not have appeared on the 1901 census. This gives us only 1 birth, but absolutely no evidence that even this one is right, until we identify her mother.

Even after all this, only got as far as the possibility of one of the missing births!!

I think that just about exhausts all possibilities, unless anyone has any bright ideas.

I have also been unable to find her, either as Mary, Mary Elizabeth or Elizabeth BULLOCK in either of the 1881 or 1891 censuses, but may find her with the identity of her mother. Looking for her may find Mary Elizabeth by birth year, even if under a different name – funny spellings sometimes, eg Emy for Amy and Elda for Hilda!

Therefore, awaiting pdf copies of the births of Mary Elizabeth BULLOCK in 1875 and Margaret Ann BULLOCK in 1894!