Transportation is limited in Churchill. You have cabs, buses, a rental car, or your own feet. I did not rent a car, so this is based on mainly buses. My first night, I took the train into Yatton and attempted to take a bus to the inn. After 10 minutes of useless searching, I was unable to locate a bus stop, so I called up Churchill Cars, a family-run taxi company. Normally, they are reasonably priced (or so I'm told), but since I called at the last minute, it ran me 12 quid for a 15-minute ride. I later found out that to take a bus to Churchill, you need to take the train to Bristol Temple Meads and take the bus from Bristol. It will run you 3 quid for a 30-minute bus ride.
If you happen to stay at the Mendip Gate, there is a bus stop almost directly across from the Mendip. Make sure you flag the driver down, or he will drive right past you, as I learned while I was staying there. There are a few locally run taxi companies, but book in advance to avoid outrageous fees.