The information that I have shows that William Smith Bryan's, father was Frances Bryan II, b. ABT 1560 who married Ann Smith, b. ABT 1560. His father was Francis Bryan, I, b. ABT 1490, d. 2 Feb 1549/50 - not known who he married. The next generation shown is Thomas Bryan II with unknown wife, then Thomas Bryan I who married Margaret Bowsey.
I do not have proof for this information which was gathered by Neil Smith. He has a geneology page or you can reach him at firstname.lastname@example.org
I feel sure that most of these are probably church records but that is just a best guess. Try getting in touch with Neil Smith and if you find something interesting be sure to post it.