I do either/or (well, I would say "I have bipolar disorder" for grammatical correctness. Wouldn't say "I have blue" I'd add the "eyes" to the end of that.). I don't feel like saying "I'm bipolar" defines me. I don't avoid saying "I'm hungry," or "I'm a New Hampshirite," so why shouldn't I say "I'm bipolar"? It is a part of me--I don't deny that. I accept it just like I accept my height and skin color and my shorter right leg. If other people want to add that as a judgment, that's on them.

Take a cold. People don't shy from saying "I'm sick." Sometimes they say "I have a cold," but no one tries to correct someone that says "I'm sick" to convey the same point. It might even be better because who knows if it is a cold or something else causing the illness.