We are booked on a cruise that terminates in Southampton. On our bucket list is spending a week, or more, in a Cotswold village. Looking for a recommendation for a location, we will not have a car, willing to ride buses. Can take to the train to our destination.
I think you should aim for Moreton in Marsh on the train
You can get there from Southampton with a change at Reading in about 2 hours
The cheapest tickets are called Advance Single where you have to travel on the booked train and i can see one in April for £23.70. If you can't see these tickets you are looking too early
Suggest you have a look at www.seat61.com for information on rail travel in UK
From MiM you get local buses to surrounding towns such as Chipping Campden and Stow on the Wold. Also outside the Cotswolds to Stratford upon Avon
We stayed in Chipping Campden at the Volunteer Inn. I highly recommend it.
Doing the Cotswolds without a car would be difficult. Consider renting a car at Oxford for the week you are in the Cotswolds.
There may be some public transportation, but before you make these plans, do your research and determine how you are going to visit the many towns and small cities of the Cotswolds.
I was in the Cotswolds last October without a car. Bus transport is very thin. Only train station is in Moreton in Marsh. I took the Go Cotswolds tour one day and saw many of the villages. I stayed in Chipping Campden and took a taxi back and for the Moreton. It is a lovely village and I thoroughly enjoyed just walking around. I had stayed in Bath earlier in my visit and took a Mad Max tour which took me to Stonehenge and a couple southern Cotswold's villages.