An acronym turned word popularized by the Orange Countyduo called The Millionaires, standing for the quote "Bomb Ass Pussy" in the song Party Like a Millionaire.
To gently and playfully. Usually on the nose, cheek or head. Bapping someone is usually done out of affection or playfulness and sometimes passive aggression.
Girlfriend: *baps you*
Boyfriend: Heyyy. Stop Girlfriend: Pay attention to meee *baps on the nose*
Boyfriend: You're such a weirdo, stop or I'm gonna tickle you