I've been to Kyoto several times (without a bike), I just walked and used public transportation. Take note though that Kyoto is strict on bicycle parking. They will really take your bike and you will end up paying extra to the rental place if that happens.
To clarify, I am looking for road bikes - perhaps "racing bicycle" is a better term (although they would not be used for racing)? - to ride in the mountains around Kyoto.
They will not be used for sightseeing.
I've a couple of friends coming over from England next month who ride a lot in the UK and would like to ride in the mountains around Kyoto but don't want to bring their own bicycles.