Bridgham exists as a family name - a search on http://www.google.com/ throws up a good number. Joel Bridgham has researched his family history and produced a genealogical chart at:
http://freepages.genealogy.rootsweb.com/~bridgham/
and he himself appears at:
http://freepages.genealogy.rootsweb.com/~bridgham/d0020/g0000034.html#I0001
His ancestor appears to be Henry Bridgham, born about 1583 in Thelnetham. It is likely that his father (unknown) was born in Bridgham and moved to a neighboring town where he introduced himself as "Henry, of Bridgham."
This is conjecture - it would be nice if anybody can substantiate it ...