Umm... No she's not. Add the word "disorder" next time you want to label someone as a mental illness. That would make you say, "She's Bipolar Disorder." Now does that sound fair? To label someone as the root of millions of people's problems?
Now try saying it with "has" instead of "is." "She has Bipolar Disorder." Much better.
You wouldn't say it with any other mental illness, so why do it with Bipolar Disorder? I've never heard anyone labelled as depression. It's always that they have depression. Why, then, am I labelled as the illness itself and you are not?
Think. Learn. Don't get hit in the face.