[Dean E]

Plausible answer for sure, but why wouldn't the bar shake ALL the time, not just on small bumps? It seems to happen mostly when crossing crappy RXR tracks and the warning bumps when approaching intersections and traffic lights.
It shakes on roads where the top layer of tar has gone away and left a shallow pothole also. Just the small shallow bumps cause the shaking. The worst spots are the warning slots on the shoulder of major highways. Not that I'm over on the shoulder much, but when I need to pull over, it's almost uncontrollable for the few seconds that I'm crossing the warning slots.

How many miles on the bike? Have you ever had the fork oil replaced? @RACNRAY has noted that the steering hub bearings up front are fairly small and can be imprinted on the bearing race. He can correct me if I'm wrong here but I believe you can check for this by putting the bike in the air and move the front end slowly left and right and feel for a catch when the bar in the straight ahead position. If you notice this you might want to have the bearings up front in the steering head replaced. Dean

 

[Dean E]

BTW, there is NO wobble in the front AT ALL!!
I've had tire wobble in the past, and this ain't that. Any Wobble, esp the dreaded DEATH WOBBLE, is a very scary situation. This shake is not as un-nerving as the wobble, but at the same time, it is quite startling when it happens.
If I could measure the shake distance from the "UP" position to the "DOWN" position during the shaking, I believe it would be about 1/2" to 3/4" of total distance of movement up and down, possibly a little more.

Doing the neck bearings will be a fairly costly endeavor. Is there any way you can jack up the bike and do the check I was talking about first to verify this might be your issue? Honestly if you do change out the neck bearings this would be a perfect time to do the forks also. D