Check your fork seals for leaks. I replaced mine at about your mileage.
also look at the condition of your rear tire too. Dial up your rear pre-load as others have mentioned.
Air pressure is key. Hard tires bounce, soft tires bounce less.
Hard tires you will feel every bump and crack in the road. This will amplify the vibrations you feel in the handle bars. You are riding on a small patch of rubber so cornering will feel crisp and it is what Canyoneers love.
Soft tires will make the bumps and cracks in the road disappear. This will dampen the vibrations you feel in the handle bars. Cornering will feel a bit sluggish but you will have more rubber on the road. This makes the bike ride like a Cadillac and is what long distance riders would prefer (if they only knew).
Many here ride with 40+ psi in their tires. I used 32 psi when I had round tires, but now that I have a flat tire in back, I run 26 psi on both. I am at 120k, she rides smooth as silk and what is this vibration you speak of ? I can let go of the handle bars at any speed (which I have tested at safe locations and conditions) and she tracks fine.
Friday, I will be burning 1,024 miles to Timberline lodge, Mt Hood, OR to attend a conference on Saturday, then Sunday I will have to return by a different route....2x IBA weekend, Yea.... Thanks to the ST1300 I will be no worse for the wear, but I will have a lot of bugs in my teeth......