Since all the census records I looked at for William say he was born in Indiana, I think that George L. Bishop is probably his father.There was an old post on the Bishop forum with someone looking for George and his wife Mary F. DeHoney Bishop of Morgan Co., IN, so this would fit with the G.L. and M.F. Bishop found in 1880 in Jackson Co., AR and the George L. found in 1870 in Morgan Co., IN.Note that G.L. had a son "C.C.".In 1870 in Morgan Co. there is a Christopher C. Bishop, age 33, also born in NC - probably a brother to George.
In 1860 Chris Bishop and wife Julia are found in Alamance Co., NC.
In 1850 in Alamance Co. there is this family: Lot Bishop, age 43, b. NC Elizabeth "Betsy" (maiden name Patram/Patrum), age 47, b. NC, married 29 Jan 1828 Guilford Co., NC (this info from WorldConnect) Mordecai, age 20 William, age 18 Eliza, age 17 Christopher, age 16 Martha, age 13 Iowa, age 10 Lot (George Lot), age 7 Elizabeth A "Betsy", age 4 Living two houses away is John Patram, age 45, wife Betsy, age 43, and Mississippi Bishop, age 10 (twin to Iowa?)
WorldConnect info states that Lot was in Orange Co., NC in 1830 and Chatham Co., NC in 1840, but I didn't verify that info.