I could be completely wrong but it's my understanding that bleach breaks down quickly. It turns to salt (2NaOCl --> O2 + 2NaCl) when it breaks down. I wash mine in the washing machine on hot/cold and then set them in the sun to dry. I then use them as needed (sometimes within hours). I've never noticed any ill effects.
I echo your understanding of what happens when bleach is exposed to air: it breaks down into oxygen and salt.
There is NO reason to fear using bleach with filter socks. The key is making sure they air-dry throughly before you use them.
I'll wash a batch as soon as my last "clean" set has been swapped in. As a result, all of the clean socks sit out for several days before any of them are put back in the tank. In practice, though, 24 hours is plenty long enough.
True fact: you can make clean drinking water out in the wild by adding 2 drops of bleach per liter of water, agitating it, and letting it sit for an hour. It's drinkable and bacteria-free at that point (but technically could still contain parasites).

