How much pressure are you using, and how does your loaded ride height compare to unloaded?
Some people love air bags, but what you're experiencing I think is fairly common. Those air bags are small and have very little air volume. If they are inflated to high pressure and hit a large bump, there simple isn't much room to expand and the "spring rate" increases significantly. They will push the axle back down with a significant force. Imagine bouncing an over inflated four-square ball and a slightly under inflated ball. Too much air in the bags and they literally are bouncing back, your shocks aren't design/valved for that kind of force. It isn't that air bags CANT work well, but I think in many circumstances they may need to be matched to custom shocks that have stiffer rebound valving (particularly if you're running high pressures).
As mentioned above, one thing I would suggest trying is reducing the air pressure and allowing the springs to sit on the overload, if you haven't already. On my f150 I had bilstein 5100s and Firestone air bags carrying a camper, and actually found that the combination worked pretty well when I dropped down to about 30psi and allowed the overload spring to be engaged. If you're inflating the bags so much that you are maintaining unloaded ride height it is going to be harsh. Try it out. It's free and only takes a minute. If you notice improvement, you can always upgrade the spring pack with an extra leaf, or with a heavy duty spring which will reduce the amount of air in the bags and likely improve your ride. I'm always a fan of keeping most of the weight on the leaf springs and mounts as designed. Use air bags to supplement as needed, but I don't like to rely on them. If you're driving around with 80psi in the bags on weak springs and one of the bags gets destroyed, it's going to make an interesting drive home.