Hi Cheryl and Barb... I'm glad you both are planning a trip to the Cotswolds! It was really the first place in Europe that I really connected with, and I think you will love it.
We've been traveling to the Cotswolds since one of our early European trips in 1997 and have spent about 14 weeks total since that time, including six weeks last summer. We've rented cottages in Blockley and Chipping Campden, and we've hosted five groups based in Chipping Campden. We've also done two long distance walking trips where we stayed in a different village every night... one a circular walk in the Northern Cotswolds (that included three nights in Stow) and the other (just this past summer), the 102-mile Cotswold Way walk from Bath to Chipping Campden. So I know the northern Cotswolds best, but I've seen a lot of the rest of the area too.
The northern Cotswolds is really beautiful, but some villages are more touristed. We enjoyed what we got to know of the southern Cotswolds this past year. Pauline really is the expert and has given you a good list of villages to consider from my perspective. We like Chipping Campden because the village is really lovely; there are plenty of restaurants, shops and services that you need for a more extended stay; and it doesn't draw the tour-bus traffic that we've seen in some other places like Stow-on-the-Wold or Bourton-on-the-Water. Even Broadway-- beautiful-- is a bit too busy for me during midday. You'd find a lot of rental cottages in Chipping Campden... it's an interesting village with friendly local people.
Despite my comment about "tourists," you'll find parts of the Cotswolds very rural. There's a lot of farming still going on. And there are tiny villages that may have only a phone booth, perhaps a pub. We rented a cottage in Blockley on our long trip in 2004. We really liked the village, but it was very small... two pubs and there was a village shop, which is really a plus. (But the walking around Blockley was great.)
If you like gardens and walking, this is the place. You could visit two gardens a week, each different in their own way, and get some good exercise visiting the gardens. The hiking is great too with a well-marked trail system.
I'll also say that the driving takes quite a bit longer than it may appear on a map. Some of the roads are very narrow and it can just take a long time to get places. I would get a good guidebook or use Pauline's Cotswolder website and start marking places you really want to visit on a map of the area. Then think about where to base that will enable you to see/do what's most important to you. Wherever you base, you'll find plenty to enjoy nearby. If you're driving on the other site of the road, you may not want to do a long day trip every day.
About buses... We have used buses a bit from Chipping Campden and had our daughter and her friend using buses a lot when they were with us one summer. There are also taxis that can be pre-booked to get you some places if you don't have a car, though that's not cheap. If you think you can drive, I would get a car. You'll have so much more flexibility to go where you want when instead of having to plan your life around somewhat-limited bus schedules. But you could find plenty to see and do from Chipping Campden using buses, taxis and walking, and I'd be happy to help if I can. The train from London does come to Moreton-in-Marsh in the northern Cotswolds, but I wouldn't recommend staying there as a week-long base.
Kathy