Because a motorcyclist is outside no-fault, your own auto policy does not automatically pay your medical bills after a crash — you rely on your health insurance, medical-payments coverage if you bought it, and ultimately the liability claim. That is the bad half. The good half: the "serious injury" threshold of Insurance Law §5102(d) only restricts covered persons. A rider can sue the at-fault driver for pain and suffering without clearing the threshold that blocks so many car-accident plaintiffs. In practice motorcycle injuries would clear it anyway, but skipping the threshold fight removes the defense's favorite summary-judgment motion from the case.
The rest of the framework still applies: pure comparative fault under CPLR §1411, the 3-year statute of limitations under CPLR §214(5), and suit in the New York State Supreme Court for the county where the accident occurred for the county where the accident occurred crashes.