There are two very different ways of doing it that I know.
The fast and dirty way is Alan's "crash and pray". You just need a piece of carpet. You throw the top as hard as you can on the carpet so it hits with the side of the body. The strains caused by the bounce will push the cap out. You will probably need to throw it several times to get it completely out. The
only disadvantage of this method is that you may end up with a cap but no body as it may crack. In fact, if you drop a bulldog sidewise on tile it will easily crack, so the carpet cannot be too thin. But if it is too thick it will not work either. By the way, I used this method to separate (a little) the Throwback to look at the brass ring. But in that case as the body is metal there is no risk of it cracking.
A safer but much more elaborate way is the one I came up with. The big caveat is that you need a shop press. The cap of the bulldog fits inside of the body, so that leaves a lip the thickness of the wall that I use to push the body. To do that I first cut a hole in a piece of wood (using a hole saw) so the cap can go through but not the body. I take out the tip of the top and place the bulldog upside down on the hole in the wood and the whole thing on the shop press. I insert a rod (actually an Allen wrench) through the tip hole, slightly slanted so that it rests on the cap just to the side of the cap hole. Finally I use the press to push the rod that pushes the cap out. It is a little scary when you are doing it but I have opened at least ten and had no body breaks. There was one bulldog that I could not open because the plastic of the cap was too soft, but it was an unusual clear plastic. I once used this method to separate a double tip bulldog as somebody wanted to make a double tip HP.
If you send it to me, I can separate it by either method. But I cannot give you a 100% guaranty that you'll get the body back in one piece.