Riding Bitch usually refers to an individual being forced to sit in the middle of the back seat or in between the two front seats in a two seat car. If they don’t call shotgun, the smallest person in the group will have to ride ‘bitch’.
This position in the vehicle can be enforced at any time by the owner/driver of the vehicle.
Also riding bitch can refer to any passenger on motorcycle or scooter, behind the driver.