Steve, you are welcome.
I certainly see where you are coming from, with you trying not to jump around changing hotels.
I did not know (when I wrote my other post) that Oxford would be your last stop on your trip; so yes, it makes perfect sense to stay there as a base and travel to Bath as a day trip.
Since you're using Oxford as a base, I'm sure you're aware that a coach (bus) leaves Oxford and goes directly to Heathrow. Convenient to take this early on the day of your flight out.
About Cotswolds tours; I highly recommend this company:
Go Cotswolds tour company, leaving from Moreton-in-Marsh, a Cotswolds village that's a short train ride from Oxford:
https://www.gocotswolds.co.uk/
GoCotswolds is owned and operated by Tom and his wife, natives of Stratford-Upon-Avon. We have taken their tours several times and been pleased with them.
They have two trips doing different villages:
https://www.gocotswolds.co.uk/product/cotswolds-in-a-day/
https://www.gocotswolds.co.uk/product/secret-cotswolds/
And another trip with a walking tour of villages.
and a trip that goes to Bath, as well as a couple of Cotswolds villages:
https://www.gocotswolds.co.uk/product/bath-southern-cotswolds-tour/
You may want to take this tour to Bath instead of the train, because the Go Cotswolds tour goes to Castle Combe as well, and you had said you really wanted to see it (on your other thread).
It sounds like a great trip you have planned! Best wishes.
P.S. You are better off taking these tours around the Cotswolds, rather than piecing it together by bus and taxi (no Uber in the Cotswolds). Reason is, the tours take you directly and quickly to the villages of interest, so you see more, and spend less time waiting around for a bus from one village to another....time consuming, as you may wait a long time for each ride.
The tours are in a small Mercedes min van, comfy seats, AC, and commentary by the driver. You are given plenty of time in each village to walk around, take photos, get some lunch. I recommend the Broadway Deli, if you take the tour that goes to Broadway.
You'll be glad you chose one of these tours rather than piecing it together yourself...I was.
Again...best wishes & happy trip planning!