Sometimes people say, I won't bite, when they want a person to be less shy and come close for a hug or whatever. You would say I will bite as a warning of a literal bite. This may or may not be a joke. It depends. You should be able to tell which is the case at the time.

I'll bite = I will get angry.

I'll bit = I'll take the bait. It comes from fishing, where a fish looks at the bait in front of him and then decides to bite. Person 1 throws the bait "Now I remember what I did", and Person 2 gets curious and "bites".

It depends on the context. Can you give us some? What else does it say? It could be a warning not to annoy someone too much, or it could be related to fishing, and you may be saying you're easily fooled.