Shims are a temporary solution. The better solution is to sand the barrel channel. Take a 1" dowel rod and wrap it with 120 grit sandpaper (I stapled the sandpaper to the dowel rod). Run it back and forth from the first lug toward the muzzle end with even pressure. With the buttstock against the floor or table, refasten your barreled action to the stock and run the dollar bill test (make sure you are not resting the stock against anything when you do this). Note where you feel resistance (if any), and go back to sanding those particular spots by hand (w/o dowel rod). Just be careful not to sand too much. Repeat until you can run the dollar bill with no felt resistance. Then, place the gun in a gun rest or lay it in some manner where there is pressure on the forend of the stock, and the run the dollar bill test again. You will likely encounter resistance. This is fine. The point is to demonstrate that, when shooting, you should have the gun resting as far back towards the breech as possible.

Most of this I learned from messaging with Sabotloader, so (hopefully) I'll save him a little typing time here.

You don't need to bed the action at the same time. I have not yet bed my action and I'm not sure I will. I find that with a muzzleloader I'm apt to remove the barreled action from the stock much more often than I would a centerfire rifle.