It seems that there are 2 kinds of bus line in Kyoto, one is Kyoto ''City'' bus and the other is Kyoto ''JR'' bus.
Most bus you could see in Kyoto is Kyoto ''City'' bus. (I did not know ''JR'' bus before I read this question)
If you use Kyoto ''City'' bus, I also recommend to buy 1 day ''City'' bus free ticket(I think this can not be used for ''JR'' bus)
http://www.city.kyoto.lg.jp/kotsu/page/0000028337.htmlThere are also 1 day free subway ticket. So, you need to take care, the design of the card is very similar.
At the first time you use this card, you need to make your card go through the card reader when you get off the bus, then the date will be printed on the back of the card.
The next time you use the card, you just show the date stamp to the bus driver when you get off the bus.
You could buy this card (probably) at any subway station(even though this is bus card) or Kyoto City bus terminal at the north exit of JR Kyoto station.
At least I could buy this card at JR Kyoto subway station(underground), JR Kyoto bus terminal(north exit of JR Kyoto station. You could find a information office at the right side of the bus terminal) and Kyoto Shijyo-Karasuma subway station(probably. it was a few yeas ago..). There are some ticket vending machines for this card at any subway stations(as far as I remember).
If you get to your hotel(Toyoko-in Gojo Karasuma) by subway (the nearest subway station is Gojo Karasuma), you could buy this card something like ''Kyoto sight seeing information booth'' around at the subway ticket gate in JR Kyoto station.
I think this card is very useful more than subway if you want to visit many places in Kyoto, but it is really complicated. Even Japanese visitors sometimes get wrong bus.
I recommend you to print out the following bus map if you do not have ones.
http://www.city.kyoto.lg.jp/kotsu/cmsfiles/contents/0000019/19770/navi...http://www.city.kyoto.lg.jp/kotsu/cmsfiles/contents/0000019/19770/navi...It seems that the easiest way to get to Ryouanji is to use JR bus but from JR Kyoto station. But if you go to Ryouanji from your hotel, I also recommend to use Kyoto City bus from Shijyo-Karasuma.
I think the Tokyo-Inn hotel stuff will guide you more information if you ask them.