Yes, that's a Pickens County unit.

I have him as listed this way:

7th Ala. Cav., Co. I and Co. C
BONNER, William J., Private (Resident of Bridgeville, Pickens Co. Dead by 3/12/1902.)

I also have William J. listed as a Private in the (Second) Pickens Greys [as opposed to the first company called Pickens Greys, which joined the 41st Ala. Inf. Regt.]. This second Pickens Greys militia was formed for the purpose of “home defense”, and was organized at Bridgeville on 5/23/1863. It consisted of members from the ages of 15 to 60 years. This unit was actually engaged in the war, unlike many home guard units. It defeated a company of seasoned Union Cavalry, even after having a large number of its soldiers previously captured by this same Union company.

There is a William Bonner, age 21, born S.C., who is on the 1850 Pickens County census. That would be a birth year of 1828-29. That is the only William Bonner on the 1850 census. The only other person in this household is a John Bonner, age 69, born S.C.