There are 2 main bus companies on Yakushima - Yakushima Kotsu and Matsubanda Kotsu. Both have different timetables and routes. Here are the details in English for 2016-17:
Also here is a map and details of the FREE PASS.
The Free Pass allows you to travel by bus throughout your trip.
And here is a chart of the bus prices for those routes individually (in yen):
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For more information about Yakushima transport check out the one and only Yakumonkey Guide to Yakushima