Scott,
Actually the surname is neither.

Jesse Lewis Bowcock was born in Albemarle County but moved to Rockingham County before the War.

Various official documents bearing his name always show Bowcock. Land sale information, local newspaper articles, listed as an election judge in the 1880's, and his and family tombstones in Mt. Olivet Cemetery, McGaheysville, all show the name as Bowcock.

You can find his Confederate Pension request of 1911 on-line through the Library of Virginia; it is under the name "J. L. Bowcock". D. H. Lee Martz, Commander of the S. B. Gibbons Camp, Confederate Veterans, Harrisonburg, Rockingham County, signed the form certifying Bowcock as a veteran. Martz was also County Clerk at the time. It is extremely unlikely he would have signed the form if Bowcock's name had not been entered correctly.

You can do an internet search and find most of the documents referred to above.

Hope this helps in your quest.

John