Hi Nancy,
There was a rather in-depth discussion of this not long ago.  I wish the
conch-L archives were easier to search.  In brief, Bynes's disease is not an
"infection", and bleach won't "cure" it.  It does not pass from one shell to
another.  It is a chemical reaction between the calcium carbonate of the
shell and acid vapors in the air.  The "symptom" is a layer of fine white
powder on the surface of the shell.  It can affect all shells, but is most
noticeable on those with a glossy finish like cowries and olives (you
probably won't notice a thin layer of white powder on a Buccinum).  It can be
prevented by avoiding sources of acid vapors (such as certain woods and
papers), and keeping the collection in a dry place.  Moisture is also
necessary to make this reaction take place.
Regards,
Paul M.