I would actually recommend that you do talk to your psychiatrist about your diagnosis. If you were diagnosed with a physical illness vs. a mental one would you ask your doctor details about that? If not, it can be harmful in the long run.

If you feel that the bipolar diagnosis was made too casually, that is something you might want to work out. I don't believe it is good to be diagnosed with something you don't have. But it is good to be diagnosed with something you do. It's true that mental illnesses do carry a stigma sometimes, but let us not take steps backwards by denying things as a means of perpetuating it.

If you don't know what questions to ask, you can find suggestions online. Ones like what symptoms led to the diagnosis of bipolar vs. unipolar depression (or other), or are my medications typical for people with bipolar disorder, are a start.

Add on: I kind of disagree with the idea of not knowing a diagnosis, especially if it's one like bipolar disorder. Diagnoses can tag along with you and possibly someday end up in "hands that you might rather they not". If they are accurate, that's one thing, but if not, it's another.