I have never had to mention that I have borderline to an employer because for me there is a lot of misconceptions that people have about borderline and I wouldn't want them jumping to conclusions that might not be true.
If it is not asked about in your application then I wouldn't mention it at all. However what I would do is say if they ask about your weaknesses and strengths is mention what might be perceived as a weakness then.
For example an aspect of my borderline is my perfectionism, so I say "I am a perfectionist and yes sometimes if things are not up to my standard then I can get disheartened by that, however the good side to this is that I always strive to do my absolute best at all times."
I don't know what jobs you are looking for but most jobs don't expect you to tell them everything about your mental health in the application stage.
To be honest that is a very good question- what to say to an employer. For me i suffer from mood swings, so I would tell them that I have depression.
Sometimes its more important NOT to tell them everything unless you want to, and because BPD is soo complex in diagnoses and for the individual then its really up to you what you say.
Also as Personality Disorders arent classified under the discriminiation at work then its up to you what you say to your employer.
My old employers just saw low self esteme and depression so i worked with that, and thats good enough for me lol.