Well, generally a car has the ability to drive away, where a bike doesn't. So i would say that when a car confronts a bicyclist and they get out with weapons, that that deems self defense measures.
Now if you stopped and confronted a bicyclist, and they pulled a weapon, you don't have the right to pull a gun seeing as you had the ability to flee.

You have to reasonably think that your life is in danger and not have the ability to flee.
Correct me if i am wrong though. I think laws vary, so you may be able to claim self defense in protection of property.