Let the train take the strain, and visit car free. Regular services connecting London to Stroud (take the intercity to Cheltenham via Swindon).
Also it's only 45 minutes from Birmingham New Street, connect at Cheltenham or Gloucester. Head north from Bristol and change, or from Bath head to Swindon and change. Easy.
At Stroud the GWR ticket office is open most of the day and there is an on platform ticket machine. Parking? Yes.
Stroud Station, Station Road, Stroud, GL5 3AP