We would like to send bulk mail to all members except those that have purchased a specific product. Is this possible? I don't see this option, but maybe I am just missing it.

The Bulk Mailing system is currently an inclusion system, rather than an exclusion system. Meaning, you can filter a list down to include people but you cannot filter to exclude them. If this is something you will regularly be doing and want to see this in a future release, I would recommend posting in our Feedback forum for evaluation.