We do a little polishing in the dental business also, although the items are
rather small like jewelry. Several companies make rather inexpensive splash
hoods to contain the mess. Here is a link to one such manufacturer:
http://www.handlermfg.com/web/index.php?main_page=index&cPath=65_76&zenid=sk
pon7a3mjc0152rqtfdi1iac2
More effective systems use a vacuum system to suck up debris but these are
too expensive and overkill for most of us in this forum. One possibility
might be to use a shop vacuum with one of these splash guards as a way to
work indoors while polishing parts.