The main bus station in Karpathos is located in the centre of Pigadia. The station is a small open-air space with a parking lot vibe, but it gets the job done. You can find the bus schedule at a kiosk on-site. To give you a little bit of an idea I've added the schedule from last year.

Keep in mind that the public transport on Greek islands isn't always fantastic and won't bring you everywhere. Also know that in May and from September onwards, children are in school. The buses run very little as they are still used for kids to get to school and back.