Hey bowie,
It's great of you to reach out to try and improve your relationship! And to be able to take an honest look at how you've been with her and making an active effort to improve.
I have a boyfriend with BPD traits but I identify more with your girlfriend here because he is the one dismissing my feelings and invalidating my needs when he is in a crisis, so I know how hurtful it can be.
To me, what I would like my bf to do at that point, if you haven't done it already, is for him to make amends: maybe try and show her you understand why she doesn't trust you without explaining or justifying yourself (unless she asks for explanation but when my bf tries and explain his behaviour it really annoys me because he makes it about HIM again while I'd like it to be about me for once). Detail the actions you did that were problematic and say why they were problematic. Show her you have a really good understanding of the issue.
And put into practice your desire to improve by validating her current feelings like her lack of trust. There are a few tips on this website on how to show empathy, like this article:
https://bpdfamily.com/content/communication-skills-dont-be-invalidatingI am not your girlfriend so I'm only talking about what would work with me, I wish you the best of luck, I hope it's going to turn out okay for you!