We recently had a post on our ShopTalk Forum about how to control dust during vibratory tumbling. Either Walnut Shell Grit or Corn Cob Grit can be used quite successfully to burnish parts with a dry tumbling operation.
As these organic media break down (or if a fine grit is used initially) the vibrating action can send dust all over the place. Adding water to reduce the dust is not really an option (muddy Walnut Shell doesn’t burnish very well).
Something as simple as draping a rubber mat over the tub or fitting a similar mat over a bowl vibe will keep the dust to a minimum. Using a thick, heavy-duty sheet of rubber of foam and bracing it to the machine will give good dust control and keep the mat from vibrating off.
These ‘covers’ also have the added benefit of reducing the noise level of the process.