I got it to work! But the BOM isn't associative, so the first thing to do is delete the existing BOM.
In Assembly Design Workbench, go to ANALYZE + BILL OF MATERIAL to bring up a big panel. In the lower right corner, click on the DEFINE FORMATS box to customize your BOM. (note there are two colums: Displayed and Hidden)
I didn't want two lists, so I hide all the properties on the top portion.
On the bottom portion, put the NUMBER property into the Display column to add the balloon number to the BOM. Use the < and > icons to display/hide whatever properties you want. I used Number, Quantity, Part Number, and Nomencature for mine. You can also use the bottom icon to reorder the properties.
Now you can go back to your drawing and insert a new BOM that you've customized.
I think by using the bottom portion, I was able to include sub-assembly parts in the BOM.