it will depend on the timing of the busses
maybe you can take a look at the bus schedule here http://unzen.org/e_ver/access/#sec3 and see if you can make it. The distance is only around 100 minutes
there is also these link, but it is in japanese:
https://www.keneibus.jp/local/express/unzen/
http://www.keneibus.jp/local/express/unzen/timetable_unzen_20170401.pdf
