Just an FYI, your insurance will actually take care of the medical bills for the cyclist. "No Fault" doesn't refer to who's at fault in an accident, rather it's a mandatory part of auto insurance to treat injuries in an auto accident. It's also referred to PIP coverage or personal injury protection. It covers the driver and passengers in a vehicle as well as struck peds and cyclists.

I work for an insurance company, specifically in the PIP department.

Your personal exposure to paying his medical bills is likely limited. Once your PIP coverage exhausts, he can potentially use his own PIP coverage on his auto policy, and then turn to any personal health insurance. Even after all that, I still wouldn't expect you to be pursued to pay medical bills.

Now, you may be exposed to a personal injury suit, which is entirely different and which I lack experience in.

I'd recommend speaking to your insurance company, they are the best resource here as they'll be more familiar with your policy and state laws. (I work in NY, not NJ)