tour Cotswolds en route London to Bath?

As others have posted recently on this forum, the Cotswolds region is spread out and doesn't really lend itself to being appreciated in less than a day, which is effectively what you'd have if you traveled from London in the morning and needed to end up in Bath that night. As you can see from a map, it's not on the way from London to Bath. Given that you only have 2 nights, I'd say choose either Bath or the Cotswolds (e.g., Moreton-in-Marsh), not both.

There are no cities in the Cotswolds, only towns and villages. It's not really somewhere that I would consider offers anything to conduct a tour about as it would simply be driving from one town or village to the other, something that anyone can do themselves. You could hire a car, work out a route and read about the area online and there's no need to pay someone to do that for you.

First, your Cotswolds tour.

In May 2016, we spent three weeks in England. The highlight of our entire trip was the day we spent on a tour of the Cotswolds on the "Go Cotswolds" Tour, hosted by Tom.

We went to Chipping Campden, Broadway Tower, Stow-On-The-Wold, Bourton-On-The-Water, and the Rollright Stones, to name a few of the stops. Tom gave out walking maps in some of the towns, and made recommendations for shops selling coffee and cakes, or lunch. Plenty of time was given for us to walk around and take photos at each stop.

Tom was born and raised in Stratford-Upon-Avon, so he knows the Cotswolds quite well.
Tom has a great personality, and keeps the whole trip fun! Not a dull moment!

On Sundays, Tom picks up at Moreton-In-Marsh station for the tour. (£35 per adult)
Tours start at approximately 10:00 am, and finish at approximately 5pm.
"Go Cotswolds" Tour is highly rated on TripAdvisor. (Trip Advisor Certificate of Excellence)

You don’t need to hire a car to visit the Cotswolds. Just contact Tom through his website, and book a fun day tour in the Cotswolds. http://www.gocotswolds.co.uk/
Click the red "Book Now" button on this page to sign up for the tour.
http://www.gocotswolds.co.uk/tour-details/
Or contact Tom at phone number 07786 920166 or email tom@gocotswolds.co.uk.

See the following page, "Joining a Go Cotswolds Tour From London and Birmingham":
http://www.gocotswolds.co.uk/blog/joining-a-go-cotswolds-tour-from-london-and-birmingham/

"perhaps it would be do-able to take a train to there from London, do a bag drop, do the tour, but then what--how best to get to Bath?"

Take the train from London to Moreton-In-Marsh. Be there early on a Sunday morning, to be picked up.
Make contact with Tom of "Go Cotswolds" through his company website ahead of time, to make reservations, and to make arrangements for exactly what time he will pick you up.
Take your bags with you on the tour. Tom locks the mini bus securely at every stop.
After your Cotswolds tour, Tom will return you to Moreton-In-Marsh.
You can take a train from Moreton-In-Marsh to Oxford, then from Oxford to Bath.
For more precise train advice, wait for one of our train experts to show up here and answer your question.

Last year I enjoyed the Secret Cottage tour. It's different from most. Many did it as a day trip from London, but they had to leave London early.

The tour also leaves from the Moreton-in-Marsh train station. You would need to check with Becky about your luggage. The train station is tiny with no storage.

I'm not sure why going to Oxford to get to Bath is recommended. I went from Bath to Moreton-in-Marsh. It took about 3 hours. You would be going the opposite direction after the tour.

We used Andrew Guppy, Cotswold Walks, last August. He planned our 8 nights stay in the Cotswolds.

You can do a tour of the Cotswolds from Bath. Contact Mad Max Tours.

We are going to be in Bath on a Saturday/Sunday in July. Sunday worked out best for us to do a tour and we found that there are not as many tours running on Sunday. We did book a "Cotswold Lazy Sunday" tour with Lion Tours. The tour includes Lacock, Biddestone, Castle Combe, Malmesbury & Tetbury for a photo stop. Link for info: http://www.liontours.co.uk/cotswold-tour-full-day. The tour begins at 11 AM.

CELTIC HORIZONS: TOUR YOUR WAY THERE--I posted this question prior to our trip, and I thought I would add this update:
We ended up "touring our way from London to Bath" by using a private company mentioned in RS Britain book that offers that service--custom itineraries based on your time, destinations, and interests. CELTIC HORIZONS ( www.CelticHorizons.com ) was fabulous! For us, they picked us up at our hotel in London, and we stopped in Avebury, Lacock, and Castle Combe on our way to Bath. Additionally, we arranged for a private full day tour of the Cotswolds, and lastly, Celtic Horizons picked us up at our hotel in Bath and drove us directly to Heathrow on departure day. Making the stops along the way to Bath meant that we spent a little more than we would have for travel by train, but we really felt that it was a wonderful way to see as much as possible en route. Both of our drivers (Neil and Norman) were extremely personable and informative. Trip arrangements and payment were handled very professionally, and itinerary advice was great. I'd highly recommend them.

I did a great 4 day walking trip in the Cotswolds (staying at an old manor house in Burton on the Water) HF Holidays. HF Holidays Link

They have walking trips all over the UK and most of the lodging is in wonderful old manors.