There is actually no train running between Higo Ozu station (situated on the line between Kumamoto and Aso station) and Aso station. Substitute buses are running on a specific schedule. 

Two bus lines are running between Kumamoto station and Aso station.

• Kyushu Odan bus
• Yamabiko bus

It takes about one hour and a half to come to Aso from Kumamoto. Since the road 57 was heavily damaged because of the Kumamoto earthquake, the quickest way To come to Aso is to take the road 339 (or milk road) from Ozu city and then the road 23 to finally go back on road 57.

You can find a timetable here

Two bus lines are running between Beppu or Oita city and Aso station.

• Kyushu Odan bus
• Yamabiko bus

You'll need between one hour and a half and two hours to reach Aso from Beppu or Oita city. 

There is actually six buses a day to go to mount Aso from Aso station. Check the Aso crater line timetable here.

Several buses are running between Aso station and Aso shrine. Please see the schedule below.