RobbieTunes

Many states offer auto insurance, of a sort, for people who do not own cars, and this includes Uninsured/Underinsured Motorist coverage, and Medical Payments coverage (in your state, it's called PIP-Personal Injury Protection).

This allows you to have extra coverage for times when you operate someone else's car and the car's coverage is inadequate, or when struck by a car in most states, or when a passenger in a car and the car's coverage is inadequate. It's generally called non-owner's coverage.

I don't know about NY, but here in NC, you cannot get a driver's license until you are listed on someone's policy or have a non-owner's policy, and provide a form to DMV that they can use to certify that you have coverage.

The coverage has 3 basic parts:
1-Liability coverage, because, yes, as a bicyclist, you can cause damage to other people and property.
2-Uninsured/Underinsured coverage, because you can be the victim of an uninsured driver, or one that has a lot less coverage than needed for your injuries.
3-Medical Payments/PIP, where there is a stated amount of medical bill coverage for you, generally from $500 to $5000, for bills from an accident.

In an accident, generally you use Medical Payments/PIP to cover initial costs/deductibles, etc, because it has such a low limit. It is no-fault, and in many states, you collect it by presenting incurred bills, even if you have health insurance. In many states, they've eliminated the double-dipping part of this.

Then, if you are not at fault, and the person at fault either has no coverage or coverage limits less than your "claim," you turn to your UM/UIM coverage. That carrier, which is yours, steps into the shoes of the at-fault party, and acts as their representative, attempts to settle the claim, and then pursues the at-fault person's carrier for their limits.

The liability coverage only comes into play if you're at fault. Your carrier investigates and defends you from claims, as we like to say, "real or imagined."