Another reason for the bobbing is a problem common to all CCPM heads--control interaction. Try this: turn on your transmitter and plug in the battery; with the throttle off, move only the right stick. Move it left to right, back and forth, and in circles. Watch the 'ball' in the center of the swashplate; anytime it bobs up and down while you're only moving the right stick, you are getting unwanted pitch input to the flybar.
With a better radio, you can mix the cyclic and pitch to minimize the effects of interaction. With the stock radio you're kinda stuck with the setup they provide stock.
Aside from mixing out the interaction with my Futaba 9C, I've also set the aileron and elevator endpoints to avoid the plastic part of the swash contacting the shaft at the extremes.