What you do when you are too slow to call shotgun, and don't want to or incapable of riding bitch. It's the right rear seat found in opulent cars like the Lexus 460h and the Maybach. However, any rear right seat will do as the expression of ridin' rich guy is only sour grapes for not obtaining the more prominent position of shotgun.
Joe: I'm driving!
James: Shotgun!
David: Piss...That's cool...I'll be ridin' rich guy.