Basically, you can pay for public transportation in Kumamoto using cash or a contactless credit card.
Traffic congestion in Kumamoto City is notoriously bad, ranking among the worst in Japan. Please allow significant extra time for travel when using buses or taxis during rush hour to avoid delays.
Tokyo to Kumamoto
<Train+Bus (7h)>
Tokyo station →(4h 54min by Shinkansen)→Hakata station→Hakata Bus Terminal→(2h. by bus )→Kumamoto Sakuramachi Bus Terminal=Kumamoto-Jo Hall
<Airplane+Bus (2.5h)>
Haneda Airport→(1h 40min by plane) →Aso Kumamoto Airport→(40min by bus)→Kumamoto Sakuramachi Bus Terminal=Kumamoto-Jo Hall
Fukuoka to Kumamoto
<Train (55min)>
Hakata station→(40min by Shinkansen)→Kumamoto station→(16min by Kumamoto City Tram Route)→Karashima-Cho station→(3min walk)→Kumamoto-Jo Hall
<Train+Bus>
Hakata station→(40min by Shinkansen)→Kumamoto station→(20min by bus)→Kumamoto Sakuramachi Bus Terminal=Kumamoto-Jo Hall
<Bus>
Hakata Bus Terminal/Tenjin Bus Terminal→(2.2h by bus)→Kumamoto Sakuramachi Bus Terminal=Kumamoto-Jo Hall