getting from Premier Inn (Bath Road) near Heathrow airport to Chipping Campden in the Cotswolds

None of the above.

Chipping Campden has had no railway station since the 1960s and the best way to explore the Cotswolds is by car.

In Bath Road you are very close to the car hire facilities at Heathrow.

Practice your stick shift transmissions before leaving home, study the British driving laws and signs, stick your courage to the sticking place and drive out of the airport, turn left onto the M4 extension, circle around onto the northbound M25, a gentle veer off a few minutes later onto the M40 for a very easy drive north and west into the Cotswolds. Chipping Campden and the local associated villages are so much easier by car.

The nearest you can get these days to Chipping Campden by rail is Moreton in Marsh. You haven't said how many of you there are; with a few then probably the most convenient is a private hire car to Slough station and then train to MinM. With only one or two you could take the bus from Heathrow to Slough or Reading to pick up the train, or a local bus to Hayes and Harlington, and take the train from there changing at Slough or Reading.

As Nigel says above though, for any touring a car is much more convenient, if not absolutely essential. You can hire cars in MinM if you don't want to drive there. Alternatively, this leaflet gives details of what may be possible by public transport (you don't have to take up the 'pass').

Thanks for the information.....really appreciate your help!