Mount Aso to Takachiho to Beppu

I'll be travelling to Kyushu this Dec for 2 weeks. I plan to stay near Mount Aso for 2 days and then move on to Takachiho for another 2 days and then to Beppu. I would hope that I can get some advise on transportation (bus or train + taxi combination) that link these places. Thank you.

Starting in the Aso area, you'll travel southeast to Takachiho, and then back north past Aso to Beppu.

There are infrequent buses from Takamori, on the SE side of Mt. Aso, to Takachiho. Getting around Takachiho is walkable but they are long walks between the shrine and the gorge. The Ama-no-Iwato shrines are only accessible by taxi or tour, which run about Y2000 per person. There is a tourist info office on the north side of the bus station.

To then get to Beppu, you can take a bus from Takachiho back to Takamori, then to Aso, then to Beppu, or take a highway bus to Kumamoto and from which you get the Beppu bus. You could also take a bus from Takachiho to Nebeoka on the coast, and then take a bus or train northward to Oita and Beppu.

The best way to explore this area is by renting a car, say around the Kumamoto Airport or Beppu, driving to your 3 destinations and return to your rental start. There aren't a lot of buses on these routes.

Thank you!

So let's say I stay in Beppu, then take a 1 day tour to visit the Takachiho Gorge, is there any good tour option?