I've read from previous answers to questions that mold does not grow on cinder block (basement) walls... the mold tester we used on my Mom's basement indicated there was mold present. I realize that we need to address the issue of the source of moisture but wanted to take care of any concerns related to what the tester indicated. Besides spraying bleach on the affected area(s) of what looks blackis grey on the cinder block, is there anything else we should be using to take care of the white growth that appeared in the tester's petri dish?

There are several mold inhibiting sealants for concrete blocks, from spray on bedliner to paints to clear lacquer. Pay careful attention to the label of the different products to make sure you get the one best for that particular basement.