My therapy is, almost in its entirety, dissecting how my mother's behavior has had an effect on me.
Have you and your T (therapist) talked about boundaries and how to enforce them? It takes some practice however learning more about boundaries and what they are helps. Take a look, this really helped me... .
BOUNDARIES: Upholding our values and independenceI think a lot of what was in the problematic parenting section really applied to me. Especially about the bits where she got incredibly worse as I grew up, got my own opinions, and went off to college.
I just wanted to say here that it takes a lot of courage to take hold of your independence. This will serve you well throughout your life. Hold on to your courage.

She sees it as an incredible betrayal (as in "you ruined my life" and "you might as well go to your *real* family" if I ever mention them) that I have relationships that are strong with other family members.
Yes, it seems to trigger an abandonment fear in a pwBPD when we want to share our time with others. Having strong relationships with other family members is healthy and recommended. You mention you grew up as an only child without your father being in the picture. Have other family members been there throughout your childhood? If so, how have they helped?
She keeps calling me, sending me her bank statements (to show she needs financial help), asking when I'm coming home.
Your mother's financial situation is hers. It's ok if you don't save her from natural consequences of not taking care of herself financially.
Except I know that when I go home, I won't be able to go and do anything without her (like see my other family members, my friends, have any of my own ideas). And when I tell her I can't go home because of college, she sees it as a complete betrayal and claims I don't love her. It's really difficult to manage.
This goes back to boundaries. It's difficult when we first start setting boundaries with our parents, it can feel awkward. It's ok to say no. It's ok to spend time with others. Would it be possible to stay in a hotel or with other family members when you visit? This could give you some breathing room if you need it.There are communication skills one needs to master in order to have a more successful relationship with a pwBPD. These skills can help you when you want to say no... .These skills work with anyone you find difficult, not just a person wBPD.
Communication using validation. What it is; how to do it COMMUNICATION: D.E.A.R.M.A.N. techniqueThere are others, these are just a few to get you started. There is a lot of information here on tools and skills, take your time. You are welcome to practice these skills here anytime.
How do you decide what level of contact is okay for you?
Choosing the amount of contact you want with your parent is a very personal choice. We will support whatever you choose to do. We each know our own personal comfort level. It may help to read more about BPD and about the skills taught here so that you are better prepared, there are more listed to the right of your screen. This decision is your call.