There are one-day small-group (van) tours of the Cotswolds departing from Bath (MadMax) and Moreton-in-March, the only Cotswold town with train service. The two companies operating out of Moreton that I'm aware of are GoCotswolds and Secret Cottage. Moreton is a short train trip from Oxford, which is where I stayed. If you didn't have time for Oxford itself, you could look into staying in Moreton.
I liked my GoCotswolds tour; it got me to several small villages in one day, which would have been impossible via public transportation. I know other posters have made positive comments about MadMax and Secret Cottage.
Moreton-in-Marsh seems to be the bus hub for the Cotswolds. If you just want to do one day of hiking, I guess either Moreton or your planned starting point would be a practical base. The advantage of Moreton is that if you hit really dreadful weather and are staying in Moreton, you can hop on a train to Oxford, which has indoor attractions.
You obviously won't be able hike a long distance in one day, so even if you end up in a place off the bus lines, it shouldn't be exorbitant to get a taxi back to your lodgings. You just need to be sure you start out with at least two cabbies' telephone numbers.
Rick has some hiking suggestions in his book.