When bicyclists are riding on the road they are subject to the same rules as cars. They need to stop for stop signs and traffic lights and the law requires they drive on the right side of the road in the same direction as traffic. They have the same rights as motorists, except that bicycles must keep as close as practicable to the edge of the traveled portion of the road.
Automobiles need to yield the right of way to bicyclists because of the danger that cars pose. Too many motorists fail to check their side mirrors for a bicyclist who may be approaching from behind them on the right - especially when the driver is turning to the right.