7-10 days to Cotswold without a car

Even though you don't want to walk the entire Cotswold Way, you might benefit from purchasing the book Trekking the Cotswold Way from Knife Edge. It gives detailed directions for both north-to-south, and south-to-north travel, breaking the route into 10 major sections and a number of sub-sections. Probably more important for your purposes is that in addition to listing accommodations, pubs, and grocery stores, each major section has a list of Escape/Access points--places you can catch a bus or train. Plus it lists the major points of interest along the route, and distances between points so you can easily judge how much further you need to walk before you can reach a point where public transport is available.

There are several companies that will move your luggage for you from place to place and they will also help you plan a route. This will be the best way to combine walking with seeing a lot while not having a car. You wouldn’t necessarily have to move every night.

I would look at the on line route description, then open up google maps, and plot where bus routes actually run to and when using Traveline.

I've just been looking at this using a more advanced planner than Traveline, and it seems to me to need a lot of thought and planning as a lot of the bus services seem to be pretty thin.

A car clearly wouldn't be much use as you'd constantly be going round in circles moving it.

I get your plan, but without use of ubers/taxis I think the plan might be a bit challenging. One of these sherpa style companies who move your luggage and maybe arrange hotels may be a better option.

In earlier threads on this topic, it has been pointed out that availability of taxis in the Cotswolds is quite limited, and such taxis as exist may be booked up in advance by locals who need to get to medical appointments and the like. Therefore, it sounds as if it would not be prudent to assume you can find a taxi at the end of the day to get back to your base.

There is a company called Cotswold Walks who will pre book your B and B's, sherpa your luggage and adapt to your requirements.
I have got a sore head from trying to make this work in the way you describe, both last night and this morning. I am sceptical that it can be done, having spent several hours on the exercise.
I am sure there are other companies, but I would drop CW an on line enquiry and see what they can do for you.
Clearly if using taxis you would pre book them like anyone else.
I have to put uber, but doubt it works out in the country there.
HF Holidays, from their base at Bourton on the Water, also do such a holiday, transporting you to the start and end points each day.
But they only have 2 dates left this year- 1 in late July, the other in late September - the latter is full.

We did six nights at Chipping Campden (Recommend the Volunteer Inn).
We had a car and it took us two full days to do the Cotswolds. It is a huge area.

Ok, you like to hike, then do that for a couple of days, you might get to see a tiny fraction of the area.
Public transport, you will be wasting a lot of time.

We used Chipping Campden to do the Cotswolds, but also to do day trips to Oxford, Blenheim Palace and Stratford Upon Avon.

There is little rail coverage in the Cotswolds, perhaps there are busses. but consider renting a car for a few days. Don't miss Stratford Upon Avon.

One possible way to do this is to walk the Cotswold Way to a certain point, then spend a couple nights in that village, and repeat this until you run out of time/interest. However starting from Bath makes it more difficult since the accommodations are sparser at the south end of the trail than at the north end. Trying to do this just 2 months ahead makes things trickier also. We are hiking with another couple (all in our mid-to-late 60s), arranged our July accommodations last November, and had quite a time of it for Stroud and points south, even with our British friends' local knowledge. (They have hiked the Cotswold Way with other friends.)

We are using Sherpa Vans for our luggage transport, which allows us to walk the 12-15 miles a day needed to complete the trail in 8 days. I don't think they arrange accommodation anymore, but they do have a list of places to stay on their website, which might help in seeing what you can do. If you are able to cover longer distances each day, with rest days in between, you might be able to get to areas that have more accommodation each day. Or skip being near the CW, and plot your stays along the most frequent bus route as suggested above, then look for local walks from those points.

Thank you all so much for your recommendations. I think I will either need to do a planned walk with a company or plan for another time. 2 months is definitely not enough time for me to plan accommodations.