The BASHAM surname seems to have orginated in the Norfolk region of England.
Every Basham family in the U.S. seems to have descended from a group of
Bashams in Virginia prior to the Revolution. There is a very good web site
dedicated to the Basham family in the U.S. - here.

I have traced my Bashams to Tennessee in the 1820's. They probably came
from Virginia in the early 19th century. They lived in Marion Co., TN for
a while, and then migrated back and forth across the state line to
Dade Co., GA for the next 100 years or so.