Trust me, bleach will not hurt your deck, matter of fact, most deck cleaners are only bleach anyway.
Is this mildew or resins leaching from the wood? Mildew means moisture and to rid the mildew you need to get rid of the moisture. Get more circulation in the area. Are tree branches impeding air flow or creating too much of a canopy? I would address this first.
If the problem is leaching of sap or other chemicals, you just might wait for the event to finally stop or remove that board or boards and replace with better ones or just turn that board over.
Why don't you come back with more details as to the situation. And is the wood PT wood or a natural wood?