I think its best to let her come to you. She may return, she may not but do not chase. That will only make her lose respect for you. She will see you as weak, needy and annoying (trust me, I know). Do you want her back?
I had a girlfriend before who also had some issues, but they came out only after the two years of being together. I was helping that girl to solve all the things and she recovered somehow, later we separated and I never felt sad that we separated, it was the perfect time for us. And we stayed like the best friends since then.
I was told sometimes by different girls that I seem to lose interest in the girls after a while, that was true before my current wife came into the door. But she was saying that I am not loving/helping enough. Huge issue for us was that she understood that I had an ex who had issues and I helped her. She was blaming me that I am not helping her the same way and intensity as that girl, but that is totally not true, I took care about that girl and my feelings were only attachment feelings with empathy. With this girl I had much more feelings which I see as a Love. I never thought to marry my previous girlfriend, but my current wife I fell in from the first moment I saw her. My wife felt betrayed, she felt I gave that ex so much that I have close to nothing to give her.
I remember in my past when I was dumped by girls I was having pride and I didn't beg them to return or something, I just totally stop any contacts. Later I always got from some people information that they were saying - You see, I dumped him and he didn't show any efforts to beg me to come back, that means he was never having true feelings if it is so easy for him to just accept the situation.
I didn't tell my wife a lot before she flew back to her country, to be honest the first moments when she told me she is leaving I just said - Ok, when are you leaving? I was totally calm and easy. I think that made her angry a lot. She was saying mean stuff like all BPD are doing but I was just smiling and saying - poor you, you were together with a monster, good God soon you will have your comfort zone in your huge house and your dear friends. But I started to be not easy and calm in the last days, we didn't discuss anything as she said she is not seeing a point to discuss. So I didn't begged to discuss it. Plus, another thing - I am European, she is North American. We were in the process to move together to her country and she made me papers which she said she will not cancel, because she cares about me. I told her - sorry, what I will do there without you? And she said I am ungrateful she is giving me another time some chance and I am spitting on her. Then she said she will cancel all things I said - if you want to do this I can't stop you. But later it was a few days before she was leaving and I started to be sad in front of her. Maybe she thought I am sad not because she is leaving but because she will cancel my papers for the new country.
I remember once she told me - "If I will ever try to run away from you or leave you - stop me no matter what! It will be not me." I told her - but sorry, how I can stop a grown adult from leaving, I can't keep people who want to leave me. She said: "And you will allow me to leave? That will just prove that you have no feelings to me!"
And now I remember also in the past I was told by other girls that I am not fighting for them enough, I allow them to leave without any drama. But I always thought that all people need some space and if you allow them to leave for a while they will thank you and return. Nobody likes annoying begging guys.
but I read some BPD girls are saying - when BPD cuts you totally off from her social media and everywhere it means she loves you, and she just wants self-preservation. My wife when she was leaving she also told me she would be in pain to see my with a new girl one day, so that's why she wants to cancel my papers also. Also BPD girls were saying that they hoped in the past - if only that guy would come to them and say - "I understand you are afraid and sabotaging the relationship so I won't want you back, but I do. I forgive you. I love you and want to work this out with you, no matter what it takes".
So I think she could be also afraid I am not loving enough so I could leave, plus sometimes I was making silly jokes saying - I have a nice looking co-worker you know and I told everything what I was doing (I left that job already). But I would never cheat, we were just speaking openly about all things, but maybe I needed to be more smart and her openness to discuss things are false. She maybe thought if I am seeing nice looking girls, I am not stable partner and she is afraid of abandonment as BPD.