It is a bit complicated if you do not drive to get to Roppokan. One of the best way is to get on the highway bus from Hakata Bus Terminal (next to Hakata Staion). The bus company operating the bus is called Nishitetsu (meaning West Rail). The bus you need to take is No.34. Final destination is called Hita. But you do not go to Hita but need to get off halfway at Haki. It is about 78 minutes to reach Haki. Fare is Jpy1,340 one way. After you get off the bus, you need to take a taxi, or call the hotel to get the pick up service. It is a 5 minutes ride. There is a telephone at the bus stop where you get off. Bus company website is nishitetsu. Alternatively you can take the train, but you need to switch train one time which may even be more difficult for you.

I wonder the hotel has routine Fukuoka airport pickup service. It is about one hour drive from the airport. I suggest you contact the hotel directly to arrange the special pick up.