Nagasaki to kurukawa onsen and Beppu

I am desesperately trying to find how to travel from Nagasaki to Kurukawa onsen? Could you help me ?
From Kurukawa, I'd like to spend a few hours on Mount Aso and then travel to Beppu..Are there busses between these spots?
Thanks in advance

how to travel from Nagasaki to Kurukawa onsen?

I think the easiest would be taking the train to Fukuoka (Hakata Station) and then a direct highway bus to Kurokawa Onsen:
http://www.nishitetsu.co.jp/bus/highway/gb/guide/kurokawa.ht...

Alternatively, you could take trains to Kumamoto via Tosu and then board a bus to Kurokawa.

From Kurukawa, I'd like to spend a few hours on Mount Aso and then travel to Beppu..Are there busses between these spots?

Yes, there is a bus route that connects Kumamoto with Aso, Kurokawa, Yufuin and Beppu:
http://www.kyusanko.co.jp/sankobus/kyushu_odan/index.php

If you travel between Kurokawa Onsen, Beppu and Aso, you might also consider renting a car: buses are not extremely convenient around there, and driving your own car would give you much more options, especially around Aso. Otherwise, the Beppu��Yufuin��Kurokawa��Aso��Kumamoto journey has the most buses.