Just to clarify - the cheaper option would be to take a taxi from Park Hyatt to Kyoto Station, and then the limousine bus. I did the reverse when arriving into ITM and going to the Park Hyatt and it was fine.

If you are near Kyoto Station, you can take the Airport Limousine bus and it's much cheaper - 1,340¥ (less than $10). It takes about an hour. https://www.okkbus.co.jp/en/timetable/K/