Bicyclist probably get way more injuries per mile than motorcyclists. It's risky!
Dedicated, fully separated paths with no conflict points have very low fatality rates. Also, even in risky areas there is a net positive effect on mortality.
Cyclists have to figure out safety by guesswork. One thing that's reasonably certain is that cars cause the majority of cycling injuries (not counting mountain biking, which I'm not equipped for). I have a rule of thumb, which is that if a car can crash into another car, or into stationary objects such as buildings, then it can crash into a cyclist. So I look at where car crashes occur: Mostly on higher speed, congested roads, and especially at intersections. My first safety rule is route choice, and I avoid routes with a lot of car traffic. I rarely encounter cars on my commute to work.
From what I can tell, Europe has more regulations and fewer lawsuits.