The likely culprit is locking your elbows such that your wrists (and shoulders) are forced to absorb the bumps. I am carrying too much upper body weight (read that as a fat gut) so I was pushing off the handle bars to support the weight.
You need to get your shoulders down and elbows bent so you can absorb the bumps with your arm muscles instead of wrist/shoulder. Your biceps and triceps are much bigger than the muscles that work your wrists and more suited to absorbing the shocks of the road. Not riding bumpy roads also helps, but that is a no brainer. Think rounded shoulders, down and back, side benefit of being more aerodynamic.
For me, it wasn't enough to keep reminding myself. I don't recommend this for anyone else (i.e. don't blame me if you build it and crash) but I built a support out of PVC that sits on the top bar that I can lean on a little and reminds me to get my arms bent.
I don't have a way to post a picture, but the rest uses 4 Tee fittings, 4 Elbows, some pipe and two hose clamps. One and a half inch ID pipe fits my top bar almost perfectly and I put in a reducer to one inch for the top rest to cut down on size. I have a "travel neck pillow" strapped on it to lean against. Worst part is that it makes it harder to get on and off the bike. And you cant reach down to water bottles, so I have two cages on the vertical pipe. One tee has the top of the tee sawed in two, then clamped around the top tube with some old inner tube rubber to provide friction and protect the paint. This leaves you with the bottom of the Tee facing up so a vertical pipe can be inserted perpendicular to the top bar, A suitable length of pipe (experimentation is needed) goes up to a Tee that sits with the two remaining openings facing out the sides of the bike. Two tees join that with the shortest possible pipes and short pieces of pipe and 4 elbows make the resting area. I only glued the elbows and top portions of the last two tees, so the resting surface is glued together, but it is free to rotate side to side and the angle is adjustable.
I take it loose from the bike when transporting by car, leaving only the one tee hose clamped to the top bar when it is in my bike rack. I used a strap back to the seat post at first because I was worried about the strength, but that makes it hard to stop and put your feet on the ground. I don't really lean on it much anymore, i just remind myself that when my chest is of the pad, my elbows are bent and I'm not wrecking my wrists.
This has gotten me through 5 MS150s and training for them. People tell me I should manufacture them, but I think that liability would be too high. Again, this worked for me and anyone trying this is on their own insurance. Try willfully changing your posture first before resorting to any crutches such as I did.
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