Fortunately the transportation in the Bieszczady mountains has improved recently and when you miss the bus it doesn't mean that you have to walk another 10 kilometres (as it used to be!) and there are many mini buses operating from/to popular tourist destinations. There's also no problem with hiring a mini bus. Some guesthouses (as Podkowiata in Komancza-see my accommodation tips) have their own mini buses and they can pick you up at the train or bus station at the time you arrive and you don't have to bother about the timetables.
BUT - if you miss the bus, if there are no mini buses around and you find yourself in the middle of nowhere - DON'T CRY! DON'T GIVE UP! and try hitch-hiking. This is quite popular (esp. with youngsters) means of transport in Bieszczady.
PKP or PKS ?
The Bieszczady mountains are situated in quite a distant part of Poland but they are easily accessible by train (PKP) or regular bus service (PKS) and of course they operate more frequently in high season (even from Gdansk ) to Sanok which is a town from where one should take another bus to the heart of the mountains.Buses operate from Warsaw to Wetlina (a very heart of the mountains), from Rzeszow and Cracow to Sanok or Lesko or Zagorz). Trains are also possible and if you go from Warsaw for instance I would personally recommend an overnight train instead of a bus as it takes 10 hours. From Krakow I would take a bus.