Should I mention that I have a Bipolar disorder in my statement of purpose?
I would not put it in the statement of purpose as it is a forward looking document (what do you want to study, what qualifications do you have, why study at X university, etc.).

If you must include it, then the diversity statement is a good place.

That being said, I would recommend that you do not include it. You can mention that you “struggled with some health/personal issues” in college but are now prepared for university, but you do not need to give details beyond that. This is your health privacy at stake. You should talk to your letter writers to make sure they know they should  not disclose your personal history without your permission.

Once you are accepted, you can inquire about student health services and reasonable accommodation for your needs.