Kumamoto to Fukuoka

I am trying to find a bus service from Kumamoto to Hakata Station, Fukuoka but unable to find any. Is there a direct train to Hakata station? What train do I take and how much does it cost?
I am planning to take the Kyushu Odan bus from Beppu to Kumamoto , stay in Kumamoto for 1-2 nights to visit Takachiho Gorge and Mt Aso and then return to Fukuoka .
Would staying in Kumamoto be preferable compared to areas around Aso or Higo Ozu? The tour to Mt Aso and Takachiho meetup point is at Higo Ozu station.
Would appreciate any advice on the above.

Train to Hakata: lots of them. It's the main shinkansen line. Google/hyperdia, etc will easily give you details.

Have you thought of hiring a car? Your plans would make a nice trip, Kumamoto to Takachiho to Aso, to Hakata.

I think you are referring to Explore Kumamoto.

https://www.tripadvisor.com.au/Attraction_Review-g1023374-d9583170-Rev...

This area is quite inconvenient when you take public transport. I am surprised and pleased to know this tour. I think this is very small company so they may not offer all tours every day. So first you should write an e-mail to book the tour.

You can take train from Kumamoto to Higoozu which will take about 40 min.

http://www.hyperdia.com/en/cgi/en/search.html?dep_node=KUMAMOTO&ar...

As mentioned you can take Shinkansen from Kumamoto to Hakata.

http://www.hyperdia.com/en/cgi/en/search.html?dep_node=KUMAMOTO&ar...

Thank you both for your advice. Yes it's the Explore Kumamoto tour by Helen. I guess I will opt to stay in Kumamoto rather than Ozu and take the local train to Ozu for the tour meet up. I found the bus timetable to Hakata and since the buses run regularly and up to almost midnight, will opt to take the bus instead of the train. Thanks again!