Taking this from a food safety issue to an OSHA issue, any time that you put a chemical into a secondary container, then that container must be labeled with the name of the chemical, and the appropriate hazard information (like signal word, pictograms, or other information needed to handle it correctly) if that container is not going to be in the continuous possession of the person who dispensed it.
If you want to keep the sanitizers in bowls, I would permanently label the bowls to be compliant with this regulation (which is the GHS, Globally Harmonized Standard regulation) so that they are always in compliance.
To follow up on Charles C's astute observation, if there is a chance for chemical interactions between the two, then that warning needs to be on the bowls.
Actually, since OSHA has the force of law, it trumps food safety standards any time. :)
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