From Fukuoka international airport to the hotel takes around 20 minutes.
Cost is around 2,000 JPY.
Use train and bus:
Fukuoka-Airport Station =>( Kuko Line 2 stops) => Hakata Station
From Hakata Station at Bus Platform (B,C,D) take bus (towards Ropponmatsu or Yakuin) to Yanagibashi bus stop. It takes about 5 minutes. It is then 5 minutes walk to the hotel.
For map instruction, please visit here