I think you will have a hard time finding a bumper-pull hitch that is rated to tow the kind of weight you're talking about. I know they exist--I can find them on eTrailer.com--but they're usually aftermarket. Bear in mind that, when bumper-pulling heavy, you absolutely want a load-balancing hitch (and often, you need one in order to stay compliant with specs).
When you're doing the math, bear in mind that a nominal 15% of a bumper-pull's weight, and 25% of a gooseneck's weight, should be over the pin or ball. If you are marginal on your payload rating, this might end up being a deal-breaker. I only point this out because I've seen trucks that have extravagant tow ratings, but surprisingly small payload capacity, especially when you subtract out the weight of passenger(s) and misc junk that is riding in the cab. To be fair, all of my shopping has been in the 1/2 and 3/4 ton category, and none of the trucks I've looked at actually would tow 16k, so it may be that by the time you get up into that range, the numbers even out a bit. Your 3500 dually certainly has a lot of payload capacity.