Can I make an insurance claim for hit and run on bicycle not on property?

In general, hit and run incidents don't care about whose property they happen on. You can file a hit and run claim on someone hitting you (or your bike) regardless of where the accident happens.

Being a cyclist does mean accepting both the rules of the road, and the laws of physics. Someone in a 3000 lb car has a lot more momentum and protection than you do on a bicycle. If you (or your bicycle) get hit by a motorist, whether or not you can file an insurance claim depends a lot on the circumstances.

First, if you weren't following the rules of the road, and yeilding to traffic as specified by traffic signs, you're the one at fault in the accident, even if they're in a car and you're on a bicycle. Unlike a pedestrian, you're not assumed to always be in the right just because you're on a bicycle. Florida requires teenagers under the age of 16 to wear bike helmets, but not adults. It's still a good idea to wear one.

Second, if they hit you (or hit your bike) and then drove off, you're facing a hit and run accident. Make sure you get the license plate number of the car, if you can, and color and manufacturer. You'll need to contact your insurance for medical treatment if it's needed.

Next, you'll need to file a police report; the 'good news', such as it is, is that leaving the scene of an accident pretty squarely puts the fault on the party that left as far as the law is concerned. Once the police report is filed, you can use it, and the license plate information to contact the driver's insurance carrier and file your insurance claim.

Like any hit and run incident, if you can't identify the vehicle, and through the vehicle, identify the driver, you're going to have a vastly more difficult time processing the claim.