This area stands out as a particular scenic and good cycling area. We had a 4 day tour of the area based just north of Winchcombe. So it was day trips over some very well sign-posted cycle routes, there are plenty on the 'ternet'. I have no particular route for you.
What I can recommend is take your bike on the Gloucestershire Warwickshire Steam Railway, get off at a smaller station, have a ride back to base. We also have a good afternoon at Prescott Speed Hill Climb. This is the home of the Bugatti Owners Club. We just happened to be passing and stopped to watch the start, this was very close to the road. The marshals invited us in after I shouted to them 'If I could go next!'. The main tourest town/villages are a pain but remember you don't have parking problems. Also some of the more remote villages are just that 'remote', quieter and very beautiful.