If we drivers are supposed to share the road with bikes, and it's illegal to drive uninsured, why don't bike riders have to carry insurance? They can cause accidents too. Plenty of bikes blow through stop signs and make illegal turns without signals.
Remember that guy from your freshman-year philosophy class who was always interrupting people to say things like, "Why can't we have WHITE History Month?" or "How come there's no MEN'S Studies program?" Don't be that guy.
The reason cars need insurance and bikes don't is that they're TWO TOTALLY DIFFERENT THINGS. At the risk of belaboring the obvious, it's really easy to kill somebody (or fuck up their food cart) with a car, but the only person you can reliably kill with a bike is yourself (and even then, you usually need an assist from a motor vehicle).
Now, I know what you're saying, Rob: You were minding your own business, reveling in your proper use of turn signals, when a black-clad anarchist on a murdered-out 12-speed whizzed right in front of you doing 40 the wrong way on a one-way street.
You slammed on your brakes. Maybe you spun out a little bit. It's even theoretically possible (though I bet it didn't happen) that this irresponsible cyclist caused you to hit another car, or a mailbox, or an oxcart loaded with caged chickens.
If so, that's pretty much the only way a cyclist can "cause" an accident with actual property damage or injury: by making a car swerve, brake or do something else such that the CAR does the actual damaging and/or injuring.
I'm not saying your douchey cyclist wasn't at fault. But the "swerve to avoid" family of accidents can be caused by pretty much anything—dogs, toddlers, squirrels, runaway baby carriages. God knows, Americans are a litigious breed, but even we seem to have made peace with the fact that our squirrels don't carry liability insurance. My advice? Have another drink and forget about it.