If you visit Oxford do not try to drive into the city and park there - it is a very busy centre. Use the park and ride service - there are parking areas well signposted around the outskirts of the city and the buses into and out of the city are not expensive and ride regularly. it is a much less stressful way of exploring.
We used the Water Eaton parking area which is huge and had no problems parking there even on a work day. When we were there parking was free but there are plans to charge for parking from the end of November but even then it will be cheaper and easier to use it than trying to park in the city.
although you can travel around the Cotswolds by public transport you do see much more of the little villages using your own transport and we of course used our smart car to explore - moving from village to village and spending as long or as short a time as we wanted. No waiting for buses.
The Smart is ours but I would love the cottage!
Chipping Norton no longer has a railway station but it is well served by various bus routes including the Stagecoach S3 from Oxford which runs roughly hourly with a journey time of just over an hour. Other services connect it to Banbury and a dedicated rail connection, the X8, which meets trains at Kingham on the Paddington-Oxford-Worcester line.
The town's main bus stops are at West Street, just down from the Town Hall. The website below has links to all the relevant timetables.
We did not need a great deal of time to explore the town and eat. There was a bus back to Oxford leaving before there would be another bus back to Kingham so here is a picture I took from that bus stop while waiting to be picked up.
The Oxford bus went through Woodstock which was a nice change of pace from our ride into "Chippy".
The train to Kingham is timed to meet the bus that goes to Chipping Norton.
Picture of where the bus stops in Chipping Norton.