It depends. There are many variations of BPD.
The fact that you accept you have BPD makes it highly more likely that you can work your way to a functional and consistent relationship, but it will take therapy, and a very understanding partner.
I was in a nearly 9 year marriage with a severe BPD, who had issues with abandonment, trust, self-esteem, etc., but the big barrier was that she did not accept that there was anything wrong with her. That's why BPDs are so hard to treat, because their self-esteem is often so low that they can't accept there's a problem with them, because that's an attack on what little self-esteem they have left.
As I said, the fact that you acknowledge you have issues that could be a problem puts you way ahead of the pack. Everyone has issues of some kind, but BPD issues usually keep BPDs from accepting help.
So, yes, if you are willing to work on it, you can get there. Hope for the best and keep trying.