It just comes down to what part of speech bipolar is, which is an adjective. The noun is disorder, as in I have bipolar disorder. You don't "have" an adjective; you only "have" a noun.

It's easy to see in the examples given. The reason you don't say " I am diabetes" is just because diabetes is a noun. Instead you say "I am diabetic" because diabetic is an adjective--it's describing you, a noun. "You are bipolar--an adjective. Whereas you have bipolar disorder. That's the reason "I have bipolar" sounds so awkward. It's not grammatically correct.