My main motivation is to witness the English countryside (the rolling hills). I have 5 days total, and the countryside is the part I'm looking forward to the most. Figured I can spend 2 days in London, half day each in Bath and Oxford, then 2 days in Cotswolds (the countryside). Does that seem reasonable?

I would like to stay overnight within Cotswolds if possible, just to experience the countryside up close, and not miss the supposedly atmospheric sunrise and sunsets. Maybe find something from the likes of Airbnb.

Traveling and waiting are OK as long as the views/routes are scenic.