Start with dish soap and a wet papertowel.
Once the mold is saturated with the soap solution come in with bleach.
Reasoning: mold spores are hydrophobic, the soap works on them just like oil. Water and soap will keep spores from spreading when you spray with bleach.
The acetic acid in vinegar also breaks down oils and does a better job of killing the fungus than a non-acidic soap. Bleach doesn't do as much as you'd think.
People say vinegar is a degreaser, but nobody can explain the chemistry behind the claim. Vinegar is just as effective on grease and oils as water in my experience.
OP isn't using the soap to kill mold. It's to allow water to penetrate the hydrophobic coating and wet the mold, which prevents it from becoming airborne when disturbed by the bleach spray.
Bleach kills all microorganisms, period. What more do you want it to do?
50/50 water and sodium hydroxide, not only kills mold but leaves nice chemical burns on flesh.
The soap isn't for killing the fungus. The soap coats fungal spores and allows them to be removed with water based solutions like bleach spray. It also keeps spores from spreading as you attempt to clean.
I've heard peroxide also works well at killing the fungus.
Sodium hydroxide.
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