The A38 from Bristol to Tewkesbury or even Upton is perfectly fine. I'm not sure if it's the best way going from Wotton though.
To get through Gloucester and up to Tewkesbury my favourite route would be, assuming you come in on the A38, take the first left, immediately after the roundabout at Quedgeley and follow that road – the former A38, I guess it is – until you see a bus lane veering off to your left. Take this, then right leading to lights by a bridge over the canal. Straight on. Follow this till the docks. Cross one of the bridges in the docks then follow a path across Alney Island, through the cattle with their huge spikey horns, to Maisemore, and then follow the lanes through Ashleworth. I think this is NCN41.