I have BPD and gave had friendships with others with BPD and my first thought is keep it as simple as possible. Scratch the sex and romance and aim for just friendship, no matter if she tries to lead you on. This will lessen the amount of chaos somewhat. Also, stand firm, try and not get dragged into arguments or fights, instead just calmly express how you feel from your point of view, that you're happy to talk about it and preferably tell her that she is important to you. You'll probably never be able to follow all the mood changes so don't try, just stay where you are mentally.

Often I can feel as if I'm two different people when I feel good and when I feel bad, and often for me it's enough that the other person doesn't "fuel the fire", shows by action that they're not going anywhere and possibly reminds me of things I've said when I felt good that contradicts what I'm claiming in the moment.

I'm also wondering if she's done any therapy for the BPD, and how good her insight into herself is. If she doesn't realize the problem it's even harder to deal with it and help her. But if she is insightful and tries to get better and even has tools from therapy then ask her how you can best help her. Because everything I've written is only based on my own experience and I have a bunch of other problems too, some of which ironically helps me contain the BPD chaos.

Lastly, for your own sake, keep in mind that she might one day just end the friendship, stop responding or similar. I've never done it myself (I think, insight into oneself can be tricky sometimes) but I had a friend with BPD a few years back and she stopped contacting me, never had time to hang out anymore and I never got an answer to why. Most likely because when I noticed the change our friendship was already over in her head.