I've been hit by a car, not seriously either, just a skinned knee. It happened right in front of a fire station so paramedics were there instantly and police were called. I got the drivers insurance info and contacted her insurance company myself. I ended up giving a deposition over the phone, weeks later, which others told me afterwards was NOT a good idea without my own legal representation.

My bike is not covered by my auto insurance, possibly homeowners. I also went to see a doctor the same day to document an aching shoulder. Some injuries show up weeks later. I'd say at minimum the proper accident procedure is to get a police report at the scene and go see your doctor the same day. This will help you recover both property and medical costs that may arise. In my case, the drivers insurance covered both my property (rip in jacket and pants) and pain and suffering.

I also followed up with the police officer, get the accident number and officer name at the scene. Good thing, because the driver had also called the officer and questioned my account. The officer said she wouldn't have filed the accident report if I had not called back to check up.