I want to know how to travel from Kumamoto to Hiroshima?By train or bus via Fukuoka (Hakata Station).
I arrive Fukuoka on the first day at 8 am and will visit my friend in Beppu in the evening (I will spend few night at her place) Is it possible for me to go to Dasaifu shrine and get back in time for bus to Beppu?
That should fit in easily. The journey from Fukuoka to Beppu takes only 2-3 hours. The trip to Dazaifu less than an hour. With an arrival time around 6pm in Beppu, you should be able to enjoy about four hours in Dazaifu.