I looked up "Sweet Betsy" and found out that it's also called Carolina allspice (the name I'm most familiar with)and sweet shrub, Latin Calycanthus florida. We've never grown it, so I can't help you mich with first-hand insight, but general references you find on the web to potpourri making should be helpful.

It seems you can dry the fruit, leaves, peeled bark or whole twigs. I'd try drying each element separately and see how each works.

The only other essential thing you'd need, then, is a fixitive. Orris root (it's actually the dried root of a type of iris) is the most common type available -- you'll find many sources for both powdered and chopped root on the web. Your basic procedure would be to mix the dried Sweet Betsy pieces that you like with the fixitive (chopped root, in this case), store them in a closed container for a few weeks, and you're done.

You could add other, non-fragrant stuff if you wished, such as dried strawflowers or non-fragrant dried rosebuds or gomphrena or whatever looked pretty. Then you could use powdered orris root if you wished, since the powder would work itself into the dried flower petals.

You could experiment with mixing scents, if you wished -- for example, adding regular allspice berries, stick cinnamon, whole cloves.

Good luck. you've inspired me to try growing some myself.