Hey OP, guessing you haven't been going out long? This is a normal feeling to worry in the early stages when you're trying to figure out if the relationship is serious or not. As long as you don't act on it or let it affect your mental health - it's ok to accept you don't know someone very well and will worry, but unless they've done something wrong you need to take them at their word. It's not BPD specific, it's new relationship specific.
I believe trust needs to be earned before you give yourself fully to anyone. Everyone's great on dates and the early stages as they try to impress - but with time and moving back to normal life you get a glimpse into what someone is like. And you can decide if you want to be with them or not. I think people behaviour on nights out is a great indicator of personality. I've seen the nicest, friendliest guys become belligerent dick heads after a few pints. I've seen very reserved men become affectionate and chatty after a few drinks. Men who spend their time on a night out talking about their amazing new gf and she's the one they want to marry, and men who get Dutch courage to mesg and old flame or see what's on Tinder.
My exH would mesg me regularly on nights out but often stay out all night, do drugs and showed up in the early hours wasted. My current DH doesn't mesg me at all during a night out until he lets me know he's en route home and never gets wasted, does drugs or stays out all night. Neither cheated nor made me feel insecure or question things. And as the relationship got more serious and i established their patterns and character, I didn't worry or wonder anymore.
It's harder to trust your instinct with BPD but don't ignore it completely, trust but verify. If he goes out a lot and is always AWOL all night, forget whether he's cheating, do you want that lifestyle? If it's this once Xmas works do and a rare occasion then you might find it easier to live with. So just observe over the next months how you feel around him and whether his lifestyle is compatible with yours for the long run.