Yeah, I don't understand the stuff with the suit in this show. Batman's suit has never been invulnerable. Its tough, and I wouldn't expect the average bullet to get through in normal situations, but in pretty much every form of media Batman's suit can get ripped, torn, shredded etc depending on who he's fighting. Its not like the suit needs to be nearly invulnerable to make Batwoman a useful vigilante in the Arrowverse, Arrow's own suits weren't even really bulletproof from what I remember. It feels like a weird plot point for where the show is, like they want to take away a lot of the danger that Batwoman puts herself in, and I don't really get why they decided to do that.
It's been body armour in all the recent movies.
Batman vs Aliens vs Predator was amazing to me just because the suit was silk.