You did say road bike but anyway this my experience. I have cycled twice in Geneva.
First time I was on a short break and did not take my bike. I "hired" a bike at the lake side bike hire place. It is free, yes it is free and there is no time limit. You just have to leave a deposit. They are usual hybrid/ mountain bikes but good enough to cycle along the lake.
On the second occasion, I was on a tour across Switzerland and I had my own bike. It is very cycle friendly city. There are plenty of places to hire a bike.