Yakushima to Kumamoto

Hi
Will be coming with the last flight from Yakushima to Kagoshima airport and my plan is to go then onward to Kumamoto.

There is airport buses to Kagoshima chuo and then the shinkansen to Kumamoto but considering the cost and time (7670 jpy and about 2 hours), is there any other way to Kumamoto without this "detour"?

I understand that the flight arrives at 17:50.

There is a direct bus that costs only 3190 yen one way, but takes more time:
18:45 depart airport
21:14 arrives Kumamoto
http://www.kyusanko.co.jp/sankobus/toshikan/kirishima/table/tt2.pdf

Or rent a car and drive there in about two hours (expenses include expressway tolls, rental fee, drop-off fee, gasoline cost, parking fee).

Or hotel in Kagoshima and transport to Kumamoto first thing in the morning. Kagoshima hotels are cheaper than Kumamoto hotels.

I'd take the direct bus option as exampled by Uji. The extra 30 minutes with worth the 4200 yen savings.