Riding slow on my road bike

Use your legs like suspension and ease weight off the handlebars just as you go over any bumps/creases in the tarmac.
Don't really know what else to suggest. Your thighs can absorb/dissipate a huge amount of vibration and road noise that your bum and wrists won't cope with for long, if you use them right. Don't keep weight on your arms where possible because your wrists are far too fragile.

I use my legs as weight cariers when riding over big humps. I put one pedal down, and put my weight on my feet, and release the weight on my hands.