In my opinion, it really would be quite impossible for a person to
become sensitized to bee venom, which is injected by the sting into the
body, by breathing dust coming off a beesuit.  A person becomes
sensitized to venom by becoming stung over a period of time.  A person
might also become sensitized to the various large molecules in the dust
of a beesuit by breathing it, but this would be a different matter
entirely.

However, if a person already has a tendency to develop allergies, hay
fever, athsma, etc., then that person would be more apt to develop a
systematic reaction (anaphylaxis) to a sting.  Such a person could also
possibly develop a different (although similar) reaction to beesuit
dust.

Ted Fischer
Dexter, Michigan USA