I'm going to venture a guess that the Bethel Virginia Artillery was one Company, that being Co. D, raised in Virginia.

A couple of Google searches: Bethel Virginia Artillery, Bethel Heavy Artillery, seems to bear this out:

Captain W. Norris Coffin, Company D, 12th Louisiana Battalion Heavy Artillery (Bethel Virginia Artillery): two rifled 24-pounders is listed in the Order of Battle during the Port Hudson campaign.

George Martin