Meeting among peers who know each other - yes. Meeting of people who know you value their opinion - yes. Never seen the "flow it past you" :) ...float it past you? . Along with Ethan, I;d say the "bounce" one is the more casual. I'd count neither as formal. Try ..get your opinion on this... for more formal.

Between your two options I would say that "let me run it past you" is the most formal. "Let me bounce it off you" is more personal, as if you know that person well.