Bleach, when used carefully, may be effective at killing surface mold. However, when I started to research how to get invisible to the eye mold and it's related odor out of some unfinished wood, over and over I kept finding assertions that bleach is inadequate for eliminating mold issues for the following reason:
Mold's hypae (root structures) actually grow into wood and drywall like roots. The hyphae are not killed by bleach because bleach's ion structure prevents chlorine from penetrating into porous materials such as drywall and wood. It stays on the outside surface, whereas mold has protected enzyme roots growing inside the porous construction materials. When you spray porous surface molds with bleach, the water part of the solution soaks into the wood while the bleach chemical sits atop the surface, gasses off, and thus only partially kills the surface layer of mold while the water penetration of the building materials foster further mildew and mold growth. [This quotation appears on many websites almost word for word, but no site I looked at gave any credit to the original source of this information]
How do you get those hyphae out of the wood or other material? You need a surfactants.
Surfactants serve the purpose of significantly lowering the surface tension of water to allow a cleaning solution to penetrate porous surfaces -KleanPros
What's an example of a Surfactant? Dawn dishwashing soap.
This is why some mold cleaning guides will suggest adding dishwashing soap into your bleach/water mixture, or say to skip the bleach entirely, and just use the surfactant cleaning properties to dislodge the mold and remove it from the surface without actually "killing" it.
A mold expert who came to do mold testing at our home claimed that, depending on the species of mold being eradicated, that bleach was the "worst thing you could do" in fixing a mold problem, because it may cause a release of highly toxic mycotoxin particles. Neither the EPA or OSHA recommend bleach for mold removal under "most" circumstances.
The EPA also points out that:
Dead mold may still cause allergic reactions in some people, so it is not enough to simply kill the mold, it must also be removed.
Which goes back to that surfactant thing. If you're talking about a non-porous surface, sure, bleach may work well, so long as you use it properly (ventilate, don't mix with ammonia, etc), but if there's any possibly porous or crevice-filled surfaces, either the dish soap or a epa-registered mold-killing product would be a reasonable choice.