The IPMBA (International Police Mountain Biking Association) is the preeminent supplier of training to law enforcement and other public safety cyclists.
Cyclists do not have to ride only on the far-right side of the road. Most MVCs (Motor Vehicle Codes; including Arizona) allow them to leave the right side when … the width of the street makes it unsafe, especially in situations where riding too close to the roadway edge would encourage a driver to pass despite having insufficient room. In these situations, the cyclist should “take the lane,” that is, ride in the center of the traffic lane. — The Complete Guide to Public Safety Cycling, 2nd Edition; p. 76