I have a 2005 3500 DRW and I believe that the original owner tried to help the ride buy removing the helpers taking several springs out of the spring pack, and adding air bags.
Personally I believe that was a mistake. I put the rear springs back to standard HD (I think), I did leave the air bags on. I mainly only get bounce at bridge joints but I believe part of it is due to the factory helpers and the crappy roads. But I do still get some bounce depending on the road.
Not knowing your past experience any truck pulling a trailer will give you some bounce. If you are expecting a car ride it will not happen.
Air bags do not hurt but I do not think that it will totally eliminate your problem.
Good Luck !