I have a couple of sites I thought I would share on doing the Cotswolds by public transportion.
https://pashaishome.com/a-complete-travel-guide-to-the-cotswolds-without-a-car/
https://explorethecotswolds.com/cotswolds-by-public-transport/
In case these don't work for you here is a RS article: https://www.ricksteves.com/watch-read-listen/read/articles/the-cotswold-villages-quirky-and-quaint