Hello to you
Firstly, Hannah's place of birth would be Pinchbeck West or West Pinchbeck - one and the same but whichever way you like is OK.
John birth is registered in Dec Q 1879 at York as you know. However I couldn't find him in 1881, 1891 or 1901 either in York or anywhere else. The only BUNNAGE in York in 1881 was Hannah BUNNAGE, a servant aged 19 born in Crowland Lincs, not very far from Holbeach. The ref is - piece 4717 folio 4 page 2. I am thinking that John was probably illegitimate.
I looked up any BUNNAGE in Lincs in 1881. There were none in Crowland, but several in Spalding. Particularly interesting was Harriett BUNNAGE aged 12, also born Crowland (Hannah's sister maybe?) living with her grandparents William and Ann BROUGHTON in Spalding. ref piece 3202 foio 118 page 8. The BROUGHTONs are connected to the West Pinchbeck area.
So there is a definite connection between York and Lincolnshire. Maybe John was living as a child with some Bunnage extended family and could have been under a different surname until he married.
The Holbeach registration area covers many parishes and the only way to be sure is to buy his marriage certificate.
I hope this has helped.
NC.