Hello and welcome to the family Peepou23. I'm very sorry this happened and we all know how stressful this can be.
Has she really moved on?
The answer here is both "yes" and "no". A big part of BPD is an overwhelming fear of abandonment. It's so strong sometimes, that they'll flee a relationship if they feel like it can fall apart. Tons of self-doubt and shame come along with that since they make these decisions while they're unstable.
The answer is yes and no because BPD's usually go through a cycle, which means that she may come back to you a third time to make amends and start over. This can happen once, ten times, or fifty times if you allow it to, and that's what makes these relationships so challenging. The cycles can be broken with validation and better communicating, but it take a lot of work on your part to get to that point.
Do people with BPD move on quick or is she an exception?
People with BPD generally move on quickly because they're so devastated, it feels natural jumping right into another relationship and focusing their energy there. For them, it skips the healing process by always looking for the next thing, the next person. But it also allows trauma to build and it often backfires on them.
But I want to see her in a couple weeks to tell her some things and be honest with her, without begging or being emotional. How should I approach?
Take some time to study in the "tips" and "tools" section of this website above to understand how to validate her feelings and avoid many of the common pitfalls. Again, this will take some work since most of it is not intuitive. I hope that helps!