Question, would a bad steering stabilizer n a 2011 tri glide cause the steering to shake badly when hitting a bump?
That is a very good possibility. Depending on the severity of the bump and at what angle and speed you hit it. I would check to see if there are signs of it leaking. That is usually the cause of the stabilizer becoming weak. I had it happen on my '09 in 2011 and the service tech caught it when the trike was in for service. FYI, if your trike is out of warranty it will be an expensive repair. Even though the replacement time is less than a half hour, the part new is over $500. Good luck with your situation.
Nothing wrong with the damper on our free and at slow speeds with bumps it will still jerk the bars at times. If it does it at speed yes you may have a problem.