No car in The Cotswolds

You could go directly to Bath, spend all three nights. On the second day you are in Bath, take a tour of the Cotswolds with Mad Max Tours. Choose Tour #2 on this page:
http://www.madmaxtours.co.uk/
Bath is interesting enough to take up the rest of your time.

You wrote, "Any suggestions? I'm making myself crazy!"
This is what happens when you are making a trip plan to do a lot in a short period of time and are getting frustrated.
Believe me, I know the feeling.

If you did take the train to Moreton-In-Marsh, it is a lovely place to stay itself.
There is a bus that runs from Moreton to Stow.

You mentioned Bristol. Do not stay in Bristol, unless that is where you want to be.
It is not the best place for day tripping to the Cotswolds or Bath.

You wrote:
"Tuesday - early train to Bath
Wed- train to London- then on to Edinburgh"

You are not giving Bath much time at all.

If you have no real interest in Bath, skip it, and spend all your time in the Cotswolds.

You mentioned stopping in Oxford. Good plan.
Lovely place to walk around. Good pubs.
Be sure and see the Ashmolean Museum there.
Moreton-in-Marsh is a very short train ride away.

There is bus service from Morton in Marsh to Stow, also you could get the bus to Broadway, Bourton on the Water and Chipping Campden.

We took train and then booked a taxi to pick us up in Moreton in Marsh and take us to our Inn
in Burton on the Water.
Here is a link to a bunch of taxi services:

taxi services

Train to Moreton in Marsh
Bus 801 to Stow on Wold
Walk 4 miles to Bourton on Water, passing Upper & Lower Slaughter
Bus 801 (again) to Cheltenham
Train to London

http://www.pulhamscoaches.com/wp-content/uploads/2016/10/801-NEW_from-14th-November-2016-_Sue-edited.pdf

Train to Moreton-in-Marsh.

Spend 2 nights at Bell Inn, 5 minute walk to train station.

Take Secret Cottage tour on the Monday in between.

There are several bus routes from Moreton-in-Marsh. See: http://www.carlberry.co.uk/rfnshowl.asp?L1=MOR0010. Some even run from the railway station.

You do not have to return to London in order to take a train to Edinburgh. Direct trains go from Bristol (Temple Meads) - which is just a 15 minute train ride from Bath. They also go from Cheltenham- which is not far from north Cotswold villages. However, these direct trains go up to Birmingham and then go via York before going north to Edinburgh. If not planning to visit York, you could change in Birmingham for the west route to Scotland which knocks about an hour off going via York & Newcastle. Don’t forget to pre-book about 11 weeks out to get the lowest prices. www.nationalrail.co.uk

Regarding bus service in the Cotswolds. I don't believe there is any on Sunday and that is when you are thinking of going. And on the days they do come the times of arrivals may be an estimate! You could taxi to another town, but just a warning, when we arrived and missed the bus, it took us some time to find a taxi, and we had little luck trying to call one. If you booked in Stow I would ask who you booked with if they could help you with a taxi.

At the very least if you are doing the Cotwolds, I'd drop Oxford so you can enjoy most of two days in them, they are lovely.

I can't thank you all enough for your thoughtful replies! Great ideas all:)

I had a good experience with buses in the Cotswolds. Not like having a car, but for my time and activities, everything went smoothly.

In May 2015, I took a morning train from London to Oxford, spent about 4 hours seeing some of the sights there, then the train to Morton-on-Marsh and the bus to Broadway. Arrived about 17:30 and stayed 2 nights. Did a ramble, etc. Third day took the bus from Broadway to Chipping Camden, had about a 2 hour layover for sightseeing, and then a bus to Morton-on-Marsh, train to Oxford, and arrived in London about 19:30.

Rethinking car in the Cotswolds - even though many good suggestions here. Here is new plan and would appreciate any new thoughts - (y'all are the best!)
Stay in Bath 2 nights at Lygon Arms
Rent car early on 3rd morning and drive to Malmesbury, Stow on the Wold and Chipping Campden , Hidecote.

After very full day - drive on to Woodstock, stay the night, see Blenheim the next morning and possibly Oxford briefly before
train to London and then to Edinburgh.

Realize the very full schedule but we like a fast pace. Thoughts on hotel in Woodstock/Oxford area?

Update - found a fantastic Virgin Train rate of 16 gpb from Birmingham to Edinburgh and will take that after the Bath-Cotswolds car trip. Will have to skip Oxford this trip - something to look forward to for next time!

You will be missing two of the mist beautiful villages of the Cotswolds if you don't visit Bourton-on-the-Water and Painswick.