Brenda,
I agree it would be nice to have some reporting features in Rhino.
In your case, I would use SelName, which would report the count in the command line history, and then manually construct my BOM. That avoids having to block parts, but doesn’t give you a list for export. I like doing it that way because I can visually scan the selected parts and sometimes spot erroneous missing or extra parts, but it’s not particularly efficient.