This is a no-brainer.  Bikes are mechanical devices and are clearly banned in Wilderness areas as well they should be.  Anyone who has walked trails that are frequented by bikers can see the damage easily.  Many bikers are out for a thrill ride.  Fine and dandy.  But taking corners at speed causes ruts and erosion.  Looking for things to pedal over or jump over is even worse.  Take your bikes to the many many other places where they are allowed.