(1) Ridin' dirty refers to the act of riding on Las Vegas public transportation (namely the Deuce Bus) for an extended period of time without travelling a great distance.
(2) The act of partially soiling one's underpants and continuing to "ride dirty" as though nothing had happened.
Person 1: We've been on this bus for like 20 minutes and we've only gone a block.
Person 2: Ya, we're ridin' dirty.
Person 1: "I think I might be ridin' dirty."
Person 2: "Seriously"?
Person 1: "I dunno, I might be."