All I have on Martin Bickham is that in 1724 a Richard Bickham, reported to be a weaver and a Quaker, purchased land on the east bank of the Delaware River. He had at least three sons --Richard, Martin, and Thomas.
In 1725 a Thomas Bickham married an Elizabeth Hopper. I don't know if he was the same Thomas listed above or not.
A Richard Bickham was exiled from England to Barbados in 1685,
A Richard Bickham was taxed for a house in Kittery, New Hampshire, in 1698.
Whether any of the above Richards were the same person, I don't know.
Carlene, I would be extremely interested in knowing how you've determined that you're descended from the Thomas Bickham mentioned above. I have yet to see any documentation tracing the southern Bickhams back farther than James, or the morthern Bickhams back farther than Hugh.