IF Mary Green was born in Dec 1901 and IF Mary was born in the same area as William Bishop, then her birth should have been registered in either the Dec quarter 1901 or the Mar quarter 1902. There is only one probable birth registration for a Mary Green in the Prescot registration disrict which is:

Births Dec 1901
GREEN Mary - Prescot 8b 778
(Lancashire BMD have the sub-district as St Helens)

Note that there are plenty of Mary Green births registered in other areas.

Assuming you have the marriage certificate for William Bishop & Mary Green. It might help if you post more details for Mary Green. Is there an occupation given for her father George? Who were the witnesses?