Not as a sob story but as it being “essential to understanding me” and how it affected my interests of study and all that
Most people suggest shying away from writing about mental illness in college essays. There are many students who do it and it’s not always the most flattering portrait to paint. Is there a way you can approach the same point using a different story?
“essential to understanding you” really means positives. You have to be very careful to know how to make a challenge like this into something positive that makes you a compelling applicant. Especially as a transfer candidate, which says you aren’t satisfied at the present college. They may wonder how you tried to acclimate, etc.
How else could you approach this?
Never disclose legally protected information during application. If you need accommodations, check in with disability services. Really understanding you and a bipolar disorder may raise concerns about the difficulty you might experience. If you want to talk about your academic interests and learning skills do not need to be within the context of a disorder.
^Agree with above. Do not disclose your disorder. Write about something else. After you are accepted to the college you plan to attend, it is ok to reveal it if you need to arrange for accommodations.