A Motorcycle Suspension Method and Sway Dampening Apparatus. Rather than selectively replacing portions of the prior motorcycle dampening apparatus, the apparatus and method of the present invention replaces the conventional dampening bushing within the OEM pivot shaft assembly. The replacement combination motor mount and bushing provides at least the same durability and dampening capability the OEM device, while eliminating the “wobble” experienced by virtually all OEM motorcycles having the prior rear pivot mount design. The replacement mount and bushing element comprises at least two different plasticized materials combined into a single element. The combination mount and bushing is made partially from a softer, pliable dampening material, as well as a more durable and hard material. Installation of the combination mount and bushing element eliminates the need for an asymmetric pivot shaft orientation, since the central bore of this element is centered on the geometric axis of the element.