Lt. Bassett was a member of Company A, Cobb's Legion (Cavalry).
There is very little known about this soldier according to this site, but I believe this is your man.
http://colquitt.k12.ga.us/gspurloc/db_details.asp?rec=219
Thomas Jefferson (Jeff) Bassett was a Louisiana born lawyer living in Brenham, Washington County, Texas in 1860 and returned there after the war.
He is buried here with his second wife, Martha Josephine.
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Bassett&GSiman=1&GScid=6157&GRid=35295541&