Just out of curiosity, when was the last time she was assessed by a psychiatrist? The total lack of hygiene could be indicative of something else, for example it's an early sign of schizophrenia (which tends to show up in teenage years/twenties, and is pretty closely related to bipolar). She also needs to take her medication regularly, and it is not your responsibility for her to take it.

Either way though, this is such a very toxic relationship dynamic. You want to help her, and you feel good about taking care of her. But that also sets up an unhealthy dependence on her for you, it allows her to get away with unhealthy behaviors because she's "damaged" by her mental illness. You have to look at your side in this relationship. Taking care for someone and their needs (e.g. they cry, you listen or give them a hug, or they're happy, you feel happy for them) is a lot different than taking care of someone (making sure their emotional needs/physical needs are put in priority over yours). Think about it. In a way, care-taking is narcissistic-this person needs you, but underneath that base narcissism there's a huge amount of insecurity on your end-you need to feel like that person absolutely needs your help rather than professional, sustained help for her own issues that you are not experienced enough to deal with. Does that sound like a healthy relationship? Does this sound good for you or her?

She needs serious, serious help. And you need a break from this relationship, she needs a break. A relationship is only as healthy as the people in it. Not taking care of base physical needs-and cleanliness is one, because it has an effect on her health both short (e.g. bacteria exposure from dishes, etc.) and long term (her teeth are going to rot out, and poor oral hygiene is a risk factor for heart disease, and she might have trouble finding work in her desired field because lack of basic hygiene).

YOU are not qualified to take care of her, or help her. And the longer that you stay in this and bail out her behavior, the longer you're keeping her from independent, healthy behavior. She needs professional help, away from you, because this relationship is already so, so toxic.