In Lesvos buses operates all over island. You can easily move by bus between cities and villages. Travel by bus is safe and much cheaper than by taxi. Ticket price depends on destination and distance, start from 1.5€ to maximum 10€. Buses company KTEL serve the island. To cross Lesvos island by bus will take not more than 5 hours. Usually buses have few stops before arrival last destination.
Mytilene as main town on island have most connection with other cities on island.
There are buses connection between cities of Lesvos every day. A lot of buses go from capital Mytilene to different cities of island. Usually last bus start 6-7 p.m. Here you can learn bus schedule to plan your trip.