FreeBMD has a few Hardee's for births, marriages, and death in Bridgend from 1840 to 1846 (widened the search in case a phonetic match gave some more clues), but nothing like your Ann on there on a Glamorgan search?
I make the assumption she was born in county as I don't have access to the census at home.
Does Ann turn up on later Census returns, or does she vanish in 1851? Could we make the assumption that she may never have been registered in birth or death records? Not sure how pro-active people were back then in ensuring the procedures were followed?