Don’t pay the bill. Let the insurance company take him to court. No insurance company will go to court over such a trifling amount in a matter that would keep the jury chuckling.
If culpability is to be assessed, then let it fall upon the person who was actually at fault, by running a stop sign and entering a bicycle path with a motor vehicle. “No-fault” insurance does not normally apply to bicyclists.
Bad law to begin with, and even worse interpretation in practice.