Sounds like the beginnings of Navicular Syndrome. Head bobbing, more noticable with a rider, etc... make sure your horse is gettting proper hoof care to encourage a heel first landing to utilize the shock absorbing qualities of the back of the foot.
Make sure if your horse is shod (which in and of itself can encourage navicular problems) so that the heels are NOt being squeezed in and contracted. It may just be in the initial stages and the internal structures not actually compormised at this point, but removing shoes and a a balanced trim would probably do wonders. Of course, I'm guessing from a verbal description alone, but I see a lot of the same thing in my work.