Take a free shuttle bus operated by the hotel (every 1-2 hours between 9:15 am and 6:40 pm)
Time table & pickup location: https://www.fusaki.com/eng/access/pickup
Take an express bus to the ferry port operated by Karry Kanko (route 55, 500 yen / 30 min) or a local bus operated by Azuma bus (route 4, 35 min or route 10, 40 min, both 540 yen)
Bus station at the airport: https://www.ishigaki-airport.co.jp/en/access/bus-taxi/index.html
For FUSAKI BEACH RESORT HOTEL & VILLAS: approx. 4,300 yen / 30 min
For Ishigaki Port Ferry Terminal: approx. 3,300 yen / 25 min
More information: https://www.ishigaki-airport.co.jp/en/access/bus-taxi/index.html
Take a taxi (approx. 1,800 yen / 15 min) or a local bus operated by Azuma bus (route 9, every 2-3 hours, 320 yen / 22 min).
Time table of the bus: http://www.azumabus.co.jp/mwbhpwp/wp-content/uploads/e3a07d56b45f7c1630fda48dbbd038b4.pdf
There are several rental car shops near the airport. You need to book a car beforehand so that the rental car shop can pick you up in front of the airport to the car park.