What is the best way to go there from London and how long does it take? Is it better and closer from Bath
Cotswolds over Bath- absolutely. Cotswolds are closer to London than Bath. You could always drive to Bath from Cotswolds (or take a local bus from Chippenham, which I have done). Rent a car anywhere west of London/Heathrow (take a train from London). Oxford is virtually on the edge of the Cotswolds, or I often use Reading. I always reserve my car ahead and reserve an automatic (if you dont ask for one upfront they probably wont be available in my experience). If you are driving on the smaller roads (eg Cotswolds) you should get an automatic so you are not wrestling with manual plus driving in England.
Yes, it's closer to Bath than London. Rent a car in Bath, Reading, or some other intermediate point, and then drive to the Cotswolds and enjoy the freedom of having a car to explore the Cotswolds. You will be steering from the passenger side and shifting gears with your left hand, however. If that bothers you, you will have to jump through the hoops required to actually get an automatic transmission, since 98% of rental cars there come without automatic transmission. There's only one train station in the Cotswolds, and limited bus service. The Cotswolds can be "done," a little, by public transport. But it's one of those areas where having a rental car is a plus.
dora, which method of transport to use will depend on which of the town(s) you're planning to visit. As Kent mentioned, that area is not well served by public transport so a rental car provides the most flexibility. if you're thinking of renting a car, I'd also suggest Bath as a good location to rent. ¶ Although I'm quite adept at driving manual transmission vehicles, I tend to prefer an automatic in the U.K. I usually use a Travel Agent to book the car rental, and so far haven't had any problems obtaining an auto transmission vehicle (I do book well in advance of the trip though). ¶ If you haven't driven in the U.K. before, it would be a good idea to review some of the resources on the web regarding "roundabouts" and other conventions of the road there. ¶ If you haven't done so already, you might want to have a look at the "England" Guidebook for information on the various towns, transportation options and sightseeing in the area. Happy travels!