Is this an adequate way to deal w/ small amount of mold?

[Dustin Beam]

Hello beautiful people of BP, 

I know there are a million threads on BP about mold,  but I did try to find somethign analogous to mine,  but to no avail. 

A tenant found what looks to be a little mold in the basement baseboard in the closet.  First,  I plan to see it in person, but expect it to be mold as it looks like in the pic. 

Assuming it is,  I figured I'd clean w/ bleach water or other mold killer,  put a bucket of DampRid in the closet and ask her to keep an eye on it.  If it comes back,  I'll tear out some drywall and inspect further.  If not,  great. 

The idea is that the DampRid and cleaning the surface would keep any mold growing from the interior space from coming back.  If there's moisture problems behind the wall,  it will come back. 

Does that seem like a good way to deal w/ this?