Here's what I would do.
Start with a dehumidifier. You can't grow in a dank cellar without one, period. Dry the SHIT outta the basement.
Do your bleach thing with a mop. Floor, walls, etc. Use a scrub brush with bleach on any exposed unpainted wood that seems to be a potential host for mold.
Now go out and buy a 5 gallon pail of KILZ oil-based primer. That stuff is the cat's ass for problem cellars. I redid mine with a fucking DECK BRUSH and my mold still hasn't returned in 3 years, plus BONUS it's white, eliminating any need to screw around with hanging plastic.
It WILL make your house reek kerosene for about 3-5 days but whatever, it's worth it. Including for the value added to your house by having a dry, bright, clean white basement- that shows VERY well for potential buyers.
Mold spores, meh. The trick is to not give them anywhere to take hold. Keep your furnace filter changed every few months, keep that dehumidifier cranking, and you should be fine.