Need help Bath & Cotswolds trip

Hi,

I plan to be in London by end of April 08 and I would like to visit Bath and Cotswolds.
Question :

1) Which part of Cotswolds should I visit? I would very much like to experience the English countryside.

2) Is there any bus service or train from Bath to Cotswolds? If yes, which town do I go to? Or do I need to go back to London from Bath and catch another bus to Cotswolds town from London? Too many towns, I am confused....:((

3) Should I spend a nite in Cotswolds or should I just make a day trip from Bath?

4) Getting around - How do i go about? Can I just walk around the countryside or can I rent a bicycle?

Thanks.

Try posting on the UK branch.