I think as Trish suggested the easiest way to check Mary's maiden name would be to get Edwards Birth Cert. He was probably registered in Crediton, Q2/1838, vol 10 page 84. The only other Bradford child registered around that time was also Crediton in 1837 but unnamed.
From all that you have said the best marriage I can come up with is William Bradford to Mary Rowe 13 April 1829, Kings Nympton, Devon but as I mentioned before there were other possibles.
Colin