If the bicycle hit you because the cyclist was not adhering to the rules of the road then normally he or she could be held at fault and liable for the damages your vehicle sustained in an accident.

Cyclists are responsible for following roadway laws and thus if the cyclist hit your car from making an illegal turn, riding too close to your car, rear-ended you, etc then he or she would typically be held responsible.

If you were hit by a bicyclist then you should get a police report just as if it was another automobile or motor vehicle that had hit your vehicle. You can make a claim with your collision coverage since it is unlikely that the cyclist has insurance to cover the damages to your vehicle or deal with the cyclist for him or her to cover the costs of the repairs personally out of pocket.

If you do not have collision coverage on your vehicle which to make a claim through for your vehicle's damages and have problems with the at-fault cyclist paying for the costs of your repairs you may need to obtain legal counsel on what your state's allow you to do legally. Likely you could take the bicyclist to court and seek a judgment against him or her for the expenses you incurred due to him or her hitting your car.