Does water make bread mold faster?
Yes. Mold has to have moisture in order to grow. You don't see moldy croûtons, unless the bread used to make them was already moldy. If bread is placed in plastic bags when it is too warm, condensation forms on the inside of the inside of the bags and the bread tends to mold faster.
If in your experiment, whole wheat bread has molded faster than other breads, you should look at the ingredients used to make the bread and the processing conditions where the bread was produced. The wheat bread could have been exposed to more mold to begin with or the other breads may have used mold inhibitors.
Some breads will mold quicker than other breads, for example, homemade bread will mold faster than store bread because there are usually no preservatives required in the recipe for making bread at home. Also some brands at the stores are made without preservatives and they, too, will mold faster. Moist breads will mold faster than drier breads.