Guidelines issued by Britain's Health & Safety
Executive on Cleaning of Diving Equipment (HSE) provide
guidance on minimizing risks from microorganisms that
can be present in BCDs as well as regulator mouthpieces
and rebreathers.
Storing diving equipment in a damp condition creates
  an environment in which fungi, yeasts, bacteria and viruses
  can multiply rapidly, the HSE states. "Fungi are one of
  the most likely contaminants, and these can produce large
  quantities of spores. Inhalation of these spores can cause
  an allergic reaction in the lungs, producing potentially lifethreatening
  conditions, particularly in those individuals
  who may be predisposed to allergy."
The HSE's recommendation is to thoroughly clean and
  dry equipment, particularly those parts that might allow
  a direct path to your lungs. After a day's diving, the minimum
  recommended cleaning regimen is thorough rinsing
  of these surfaces with clean drinkable water to flush away
  minute deposits that could act as nutrients for microbial
  growth, followed by complete drying. (One popular technique
  is to partially inflate the bladder and hang the BCD
  upside down in the shade so the rinse water accumulates
  in the inflator hose. Then open the inflator mouthpiece
  and let the water drain out. Repeat one or two more times. Check your owner's manual for more instructions.) If water
  quality is in doubt, use sterile, boiled or bottled water for
  rinsing.
After drying, store in a dry, clean environment - - ideally,
  an enclosed room with circulating air and minimum
  exposure to airborne contaminants. As the microbial
  agents can be "opportunistic and tenacious," consider periodic
  disinfection, particularly of shared equipment.
HSE specialist diving inspector Steve Field noted,
  "While it's important that the disinfectant used is effective
  and safe, it's also important that it doesn't damage the
  equipment. Manufacturers employ a wide range of materials
  in their products and they are therefore best-placed to
  advise on what disinfectant is compatible with the materials
  they use."
Manufacturers' instructions should be followed carefully,
  because inhaling unrinsed disinfectant can itself pose
  a health hazard. Preferably, the disinfectant should be
  effective against the most resistant microorganism - - in this
  context, Mycobacterium tuberculosis (TB).
Mike Firth maintained that he and his friends had
  always rinsed their BCDs with a sodium hypochlorite sterilizing
  fluid. But Professor Denning feels that while sodium
  hypochlorite "is likely to have an impact on the aspergillus
  fungus, it won't necessarily kill it."