Maybe it would be enough to wipe all the surfaces down with vinegar, which you should do at least once anyway.
Another thought: instead of vinegar in a dish, why don't you try wetting a sponge with vinegar and setting that on a saucer, or something unbreakable. That way, there's nothing to spill, even if bumped, and it will give off the vinegar fumes, probably better than having an open dish because the sponge will be drying and giving off fumes from all surfaces, not just the top of the bowl. And if it's enclosed, the fumes should penetrate everything. Just a safety thought.
Here's to Success!