I just came back from Kyoto. Me and my wife rented bicycles for 3 and a half days and it was fantastic! The weather is perfect for biking.On my last they we used the bus and it was terrible compared to biking.
The only thing you need is pocket wifi and smartphone. Choose the destination and choose walking mode in Google Map. It will lead you through small street which is very quiet. Always ride on the pavement like the locals. There are some areas which are bike prohibited but I still saw people riding their bike on the pavement. So virtually, you can use the bike almost anywhere. However, I suggest you find a parking spot near all the crowded area (Gion, Kiyomizu-dera,..). Most of the itineraries have dedicated parking spaces.
Here's a map with all the parking spots I found on the internet and added some that I found during my trip:
For more maps and information with biking related, you can go to this website: http://www.cyclekyoto.com/
Again, I'd recommend bicycle all the way. Especially the peaked seasons.