Buses from Chernivtsi, Vinnitsa, Lviv or Kiev take 1.5, 4, 5 and 6 hours, respectively. The buses from Kiev cost around 85 UAH but can faster marshrutkas minibuses can be 100 UAH from Vokzal the railway station in Kiev. The buses from Chernivtsi are not as frequent as Lonely Planet may lead you to believe. The buses from Vinnitsa are rare but exist.
If you plan to go to the spectacularly located castle in Khotyn on your way to or from KP and Chernivtsi, you can visit it in route as it sits almost exactly on the route between the two cities.
There is train service to Kiev via Khmelnitsky taking 6 hours, but arriving/leaving at awkward times. A better option is the night train, which takes 12 hours.