Also, welcome!
Why in the world are you going all the way out to Shikoku Island for your first night in Japan - only to immediately leave the next day? From KIX (Kansai International Airport near Osaka,) Osaka is 45 minutes by limited express train and Kyoto is 75 minutes. Both are very easy connections from the train station located in the airport building.
Naruto-Tokushima on Shikoku Island is a 3+ hour journey with at least 3 train connections. The bus link provided by the hotel would be daunting for those of us who visit Japan frequently and speak at least some Japanese. If I HAD to get to Naruto-Tokushima from KIX after a long international flight and an afternoon arrival, I'd spend a night either near the airport or in Osaka near Shin-Osaka station, then go on to Tokushima the next morning. Kyoto, on the other hand makes a perfect first night stay.
In answer to your inquiry about bus transportation in Kyoto, there are prepaid bus/subway passes available in 1000 yen and 3000 yen denominations. Machines on the subways and buses accept the cards and deduct the cost of each trip until the value is gone. You can purchase them at the Transportation Center located just outside the Karasuma (north) exit from Kyoto Station. I always pick one up immediately upon arrival.
If your train travel will be limited to KIX-Kyoto-Tokyo-NRT, then a Japan Rail Pass would not really save you much, if any, over just buying tickets as you go. If you will actually be going to Shikoku, then I'd suggest purchasing Rail Passes. Rail Pass vouchers must be purchased before you go to Japan and exchanged after arrival for the actual Pass. Search this forum for Japan Rail Pass and see the "sticky" thread at the top of the forum. If you are NOT using a Rail Pass, there is no way (or need) to make train reservations ahead of your arrival. It is a good idea to get all your train reservations as soon as possible after arrival. Again, I usually do that at the JR Service Center at KIX.
JR