Doing a quick search I found this old response on Japan-Guide:
This is what I posted for someone in TA recently with updates for your case.
There are three ways to go to Mt. Aso from Takachiho. The bus leaves 8:31 at Takachiho.
1. There are direct buses from Takamori Chuo only on weekends & holiday.
2. Get off at Takamori Chuo(arr. 9:39) and take a scenic Minami Aso train to Tateno, dept. 9:45 (Torokko sightseeing train (470yen+500yen) on weekends+holidays Mar.1- Nov. 30) arr. 10:32 or a reg. train dept.10:28, arr.10:54(470yen).
2.1 Then, take either connecting JR train to Aso station & a bus to Asosan-Nishi ropeway station
2.2 Or the Cross Kyushu bus(Aso 1-Go from Tateno(dept.11:20) to Asosan-Nishi rope way stationi(1,120yen). See Aso 1-Go below.
3. Another is to get off at Kumamoto/Aso airport(arr.10:28) and catch a Cross Kyushu bus coming from Kumamoto to Asosan Nishi Ropeway station(Aso 1-Go dept.10:50, Arr. 12:06, 1,490yen).
This Aso 1-Go has 90 min. lunch & volcano sightseeing break from 12:06-13:36. The fare from Kumamoto AP to Kurokawa onsen is 3,850yen including lunch(1,050yen) but the cable car ride is extra. The fare is higher due to additional RT legs from JR Aso to Asosan Nishi station+lunch box.
If you get off (w/o lunch) here & take the later Kujyu 5-Go bus from JR Aso dept. 16:26, Kurokawa onsen arr.is 17:14 & 960yen
Aso volcano sightseeing info.http://www.kyusanko.co.jp/aso/english.html
As of right now, #2 is not an option as the train route between Takamori and Tateno is down. No one knows when it will be up and running again.
I do not know if option #1 would still be possible either since Takamori Station does not currently have any trains going to it.
You should be able to do #3 though, even if it involves some back tracking. It might be your only viable option without renting a car.
I admit, I am planning to go to some of the same places as you and I am renting a car. I think it will be a lot easier.