I did the Camino in May of this year. I used
http://www.cycling-rentals.com/ and was quite pleased. I brought my own helmet, pedals and bike seat and had them set up the bike exactly like the one I own. I also took extra tools, CO2 inflator nozzle, air pressure guage and first aid kit. You can buy CO2 cartridges in Spain I also brought a really loud bell to add to the rental bike.
In May about one third of the days will have some rain, so plan accordingly. Include some rest days and tourist days in addition to weather days. Make sure your bike can handle rain---waterproof baggage, fenders/mud flaps, great rain gear. Rain can make sections of the trail so muddy that you will prefer the road, or at least I did.
Do it yourself. I biked the Camino by myself. You are never really alone. There will be times when you don't see other pilgrims, but then you will likely see a car/truck in a few minutes. Every time you stop you will be able to make new friends if you try.
Ahead of my trip I only booked my pre-Camino bike days and my last day. That was so I would have a place to get over jet lag and the rental company knew where to send and pick up the bike. The only time during the trip I booked ahead was when I had my gear shipped ahead as the needed a place to drop it off. That is a good idea on those days when you have huge elevation gains.
You will do fine. Enjoy. PS get one of the Pilgrim passports form this site and enjoy getting it stamped everywhere on your journey.