getting around the Cotswold villages - bus or taxi?

There is an excellent trip report on TA about this same issue. It's from 2010 but still relevant. Check it out.

http://www.tripadvisor.com/ShowUserReviews-g186281-r54521979-Cotswolds_England.html

Rick's Great Britain guidebook states that there's no public transportation to Stanway, Stanton has only a scant and upredictable few buses, and implies no public transport to Snowshill. Without a car, you should plan to take taxis or to walk with local maps.

We are middle age and live near Canada. It is not hard driving in the Cotswolds ...you are on country roads. Don't worry about driving on the other side, sometimes you just drive down the middle. Freeways are more worrisome. As long as you can drive a stick no problem. Automatics used to be more expensive. They do have walking tours that port your bags and arrange accommodations. If you drive in Canada...you can drive in the UK. It only took my husband a day to get used to it. I was navigator.

The OP states they are not comfortable renting a car there. This is a personal and safety-related decision that each traveler is the most qualified to make.
However, as Laura's post explains, not having a car in the Cotswolds poses a significant challenge.
Over the years on this forum, I don't recall a lot of travelers who have reported they were successful at seeing a lot in the Cotswolds without a car. Maybe a couple.

I think there's only rail service to one location that is actually in the Cotswolds.

The next best option, if a rental car is rejected, might be to pay for van tours operated by companies. This will involve some expense.

Taxis would be expensive due to the distances involved, plus the difficulty and cost of getting the taxi to come back for you or wait for you while you see the site, then on to the next one, etc.

I recall that bus service is quite limited, involves significant wasted time waiting around time, and can be unpleasant if the weather is not cooperating.

The distances between lodging and various sites is such that walking would be strenuous, time consuming, and could be unpleasant if the weather is not cooperating.

Thank you to everyone for the informative replies! Your advice is VERY helpful.......we will probably take a van tour so will start the research on that now. Thanks again!

Thanks for letting us know that our advice was helpful.