Difficult without a bit more to go by ....
There are two Bertha Cunliffe's on the 1901 census but both of them would appear to be too old, unless they were adults rather than a child - could it have been somebody becoming a Catholic prior to marriage ?
Red Lion Inn, Church Street, Golborne, Lancashire
Richard Atherton Head M 30 Publican Lancashire Golbourne
Margaret Eliza " Wife M 28 " Haydock
Martha Jarre " Sister S 21 " Golbourne
Bertha Lilian Cunliffe Visitor S 17 " "
Elizabeth Ann Lucas Servant S 17 " Haydock
RG13/ 3587; Folio: 15; Page: 22
The other is Donnall Green, Ashton in Makerfield, where Miles Cunliffe is 52 a coal miner from Ashton, wife Bertha M is 51 from Clapton? London, and their daughter Arrant? 22 from Ashton.
RG13/ 3572; Folio: 163; Page: 12