What happens to the bleach after mopping?
Sodium hypochlorite decomposes by a couple of different pathways:

$\ce{NaOCl\leftrightharpoons Na^+ + OCl^-\\
2OCl^- \leftrightharpoons O_2 + 2 Cl^-}$

In that case, the oxygen escapes (if it didn't react with "things to bleach", which is of course how bleach works in the first place), and you are left with ordinary salt.

The other pathway is 

$\ce{3 OCl^- -&gt; ClO_3 + 2 Cl^-}$

In that case you get some sodium chlorate, and again some ordinary NaCl salt.

Both NaCl and NaClO3 are crystalline solids that may be blown around like fine dust; some NaOCl may also remain behind. Note that according to wikipedia most commercial bleach solutions contain a small amount of sodium hydroxide to slow down the decomposition along the pathways mentioned above.

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