It doesn't look to me as though Joseph and Sarah were married. Elizabeth's baptism on the IGI shows her as Bryant or Dix, the implication being that her parents weren't married, although unusually the father is named. This being the case, it's possible that William was baptised as Dix, if he was another illegitimate child of Sarah. And sure enough, there's a baptism of William Dix in Houghton Conquest on 10 Oct 1775, son of Sarah Dix. So there's no evidence that his father was Joseph Bryant.

David