If Ann was born around 1811 there will be no birth cert, as Civil Registration only began in 1837. You will be reliant on a parish register of a christening if she was christened.
You say "her parents are given as Arthur and Dorothy Bell", so presumably you have already found this parish register?
To find Dorothy maiden name may take a bit of detective work and wider research. First I would check the PRs to see if there are obvious siblings for Ann- where does she fall within the family? If she appears to be the eldest, then that may suggest a marriage not long before 1811. Or you may find she is the youngest of 12, for example, suggesting her parents may be in their 40s and been married 20 years before she arrived. Then you can look for marriages for Arthur Bell to Dorothy around the appropkate time, starting with the parish the eldest child was chr in, and then looking at neighbouring parishes (remember weddings were traditionally in the brides home parish even if the couple then settled in the grooms, because that was where he was working and he would be the breadwinner).
If you still find both Dorothys are still both "possibles" you may have to look for more clues, which may not be easy. Wills for example, choice of names for the children of each Arthur and Dorothy couple (compared to names of each couples parents and siblings).