Okay, assuming that that is the 1881 census you have given:
Ask for (or supply) the 1871 census details to see if Bridget is the wife/mother at that time.
If she isn't then, Bridget is a re-marriage, and you should be looking for the earlier wife.
The search freebmd for George's marriage around 1863/1865, noting the page(s) and seeing what the bride's forenames are. If he doesn't turn up, go to the original index pages, and see what brides have been transcribed for the page/district refs.
PAuline