At this point, what does it matter? He fell thirty stories and "braced" Rachel's fall in TDK by...hugging her. Taking a bullet or two isn't gonna ruin my suspension of disbelief. Also, considering how advanced his suit is, why would it be a stretch that it's bullet proof? He's facing guys with guns all the time. That would be among the first things that would be implemented into the suit. Like, a cape that can use an electronic pulse to literally change form and become a hang glider in an instant is okay, but some general protection against bullets isn't? I don't see the big deal.
Come to think of it, it's even more ridiculous trying to imagine Batman taking down scores of well armed goons without having bullet proof protection. What, does he just move really, really fast in dimly lit rooms, so that nobody can possibly get a beat on him? There should be an origin story of him going out for the first time, only to come back almost immediately, panting and hysterically screaming "Lucious! Guns! They've got guns...with bullets! How did we gloss over such a vital detail when designing this suit? I almost fucking died out there!"