Put bar ends on it, I would bet that it would cure your problem.

Why exactly are you letting go of the bar at 55+ MPH?  It sounds like the problem you're having is harmonic vibration rather than real buzz.  Harmonics is/are what makes a bell ring.  If you do something to dampen the vibration, like, say, hold onto the grips, it will dampen the harmonics.  Adding bar ends changes the harmonics and dampens the vibration.  
I used to have an 86 Chevy Cavalier Wagon.  Old style radio antena.  At 58 MPH wind speed, there was a harmonic vibration and the wave length was the same as the length of the antenna.  Up to about 66 MPH the wave length got shorter and shorter until the secondary harmonics killed the standing wave pattern.  Intersting to see a real world application of what I learned in tech school, but I digress.  
If you alter the harmonics you can kill the vibration.  Bar ends will help.  A bar-snake might just fix it for good.  Worth a look.  

Hey Kerry, do any bikes still suffer from high-speed-wobble.  I went down from that once.

tire pressure is your friend.  after reading and replying to this post i decided  I should check mine and the front was down to about 25.  bike felt so much better today to and from work that i could get it leaned over nice in my favorite twisties that i make a point to ride on every day.

Jake

My left arm is messed up from my job but to make a long story short Im left handed and riding for a while will make my hand go numb and I let go to streach my and rest my hand on the tank. Now riding with one hand I can feel the vibration and if I let ease up on my grip it starts to shake. I am getting my problem treated now and while Im off I want to get my bikes too. Everything on the bike seems smooth so I hope the bar ends will help because the short ride I took with the air pressure change made a noticable differance. Also my bars are bent on the right side just enough to hit the tank would this make a differance?

i have no bar weights on my bars, infact, i have lightweight clipons instead, and my front end doesnt shake, no matter what speed.  weight will SLOW the wobble as it takes energy to wobble. but will not stop the cause. your right about harmonics but in this case its applied BIKE WIDE, bearings, frame flex, tirepressure, spring load, dampining of shocks/forks,rubber,weght placement, and overall geometry
everything on the bike and how it interacts with its fellow parts has pull, or stores and releases pull.  when everything is right, these pulls ballence out, when something is out of wack, the pulls become no longer ballence and you have wobbles.   some little some extreme.

It sounds like this "shimmy and shake" may be inherent in the GS500. Minor in some bikes and more pronounced in others.

It's inherent in all bikes.  The longer bars can amplify the effect.  Substantial bends in the bars can help reduce the effect.