Hi there!
Good to hear you have your rail passes! Here are some answers for you:
Getting to Fukuoka from Kyoto
The bullet train terminal in Fukuoka is called 'Hakata' so you'll need to use this to search for correct routes. In order to get to Hakata from Kyoto you'll need to make 1 change (generally at shin-osaka) to change from the Hikari bullet service that runs on the Tokaido Shinkansen route (Osaka-Kyoto-Tokyo) to the Sakura bullet service that runs on the Sanyo and Kyushu shinkansen route (Osaka-Hakata-Kagoshima). The hop between Kyoto and Shin-Osaka is very quick and normally there are very quick connections. Here is a sample itinerary for you with the change at Shin-Osaka listed.
Direct from Kyoto to Osaka
There are many direct bullet services between Kyoto and Shin-Osaka (the bullet train terminal in Osaka). Osaka station in town is only serviced by normal express trains and so will require a change at Shin-Osaka to get there. If you are going to Osaka from Kyoto, I recommend you use normal express trains rather than the bullet train, which have direct trains (and are quicker!). Here is a sample direct itinerary from Kyoto to Osaka for you taking around 27mins.
I hope this helps, but if you have any further questions please don't hesitate to ask!
