I ran across this site that has lots of useful information on connecting the Cotswolds villages by bus and train. www.explorethecotswolds.com. Hope this helps some of you without a car.
It can be done, though not quickly and not all of it without changing locations. We spent two weeks in Moreton in June of last year without a car. Slow paced, saw plenty of what we wanted to see. A few of the major villages on the eastern side, a few gardens, a few trips to Oxford and Blenheim. A great ale is my favourite alcoholic drink, so no driving.
These will help:
https://www.nationalrail.co.uk/
https://www.pulhams.co.uk/busservices/timetables/
https://www.stagecoachbus.com/
https://www.gloucestershire.gov.uk/transport/the-robin/
I hope the Robin is still working. We used it twice, the only people on the bus.