To have sexual relations with someone else, usually casually. Bouncing with someone implies reaching home base. More polite than "fuck," about the same level as "bang" or "screw."
"Dude, last night I bounced this random chick I met at a party. Turns out she's my brother's girlfriend. I'm in such deep shit."
"Did you end up bouncing that hot guy you were hanging on all last night?"