Jonathan,
Captain Robert A Hardaway organized his battery and moved it to Virginia in June, 1861. The book, The Long Arm of Lee by Jennings Cropper Wise does not mention the battery until May 1862 during the Peninsula Campaign. It is not mentioned as being present at the Battle of Bull Run. Because of the proximity of the month of June when the battery was forming in Alabama and the battle being fought in Virginia in July, it is my belief that the battery was in Virginia but was probably near Richmond still preparing for field service. My records indicate the battery as being assigned to the Army of the Potomac but since the "Official Reports" also do not mention this battery until May 31, 1862 in Volume X, page 946, I believe this battery was near Manasas, after the battle, but not engaged against the union army. Another source consulted is Joseph H Crute Jr who does indicated the battery stationed at Manasas but not engaged at the Battle of Manasas. The few mentions of this battery in the "Official Reports" actually indicate the battery was not seriously engaged until the Battle of Antietam. The battery was armed with Parrott Rifles.
Hope this helps
Ron