Again, there is no train at Kumamoto Airport. I've picked up and dropped off people there many times as well as driven under it on the way east (bypassing Kumamoto City on a shortcut).
There is a bus from the airport to Kurokawa. It starts at Kumamoto Station goes to Yufuin or Beppu, but makes stops at the airport and Kurokawa along the way. The link is given on the previous message link and here:
http://www.kyusanko.co.jp/sankobus/english/table/odantt1.pdfThe bus stops at the airport at 8:57, 9:57 and 13:08 (No.1, No.3, & No.7). The 3rd bus (11:28) doesn't go to Kurokawa Onsen but only as far as Aso Station. They arrive at Kurokawa at 10:44, 12:28, and 15:39 respectively.
The Odan bus requires reservations. Contact info for this is at:
http://www.explore-kumamoto.com/getting-to-kurokawa-onsen/If you wanted you could take a bus or taxi to Higo-Ozu station, take the train to Aso Station, and pick up another bus there. If you use a Sanko bus from Aso station, there are some shuttles from the Town Hall (Yakuba mae) in Minami-Oguni, west of Kurokawa.
http://www.kurokawaonsen.or.jp/eng_new/access/#access02From the bus stop in Kurokawa, the Ryokan Wakaba has a shuttle to the hotel for their guests. Check at the info counter by the stop to ID one or otherwise take a taxi or walk. No place is that far but there are a lot of steps from the parking lot down to the river. I don't think any ryokan in Kurokawa have a shuttle except from the town bus stop as this place is a long way from anywhere.
The easiest way to go would be to take a taxi from the airport but it would be expensive. 2 or 3 people would lower the per person cost, though. The best way to see the area would be to rent a car. That way you could drive up to Kusasenri on Mt Aso, Daikanbo on the caldera edge for some views of the floor and 5 peaks, and along the Yamanami Highway up to Mt. Kuju for some views of the countryside before heading to Kurokawa.
I haven't stayed at the Wakaba but if I remember right, it has a newer exterior and is to the east upstream from the main ryokan center of town. The new place might be in front of the Wakaba, though.
Ask them. Info@toryokanwakaba.Com