Use carpet shampoo to scrub the area where mold is on or in the rug. Make sure that if there are any black spots, you scrub them until you have removed them.
Using clear water, remove any remaining soap left on the rug. Use the shammy to soak up any remaining water in the area.
Set up the box fan on high so that it is directed towards the spot you have just scrubbed. If it is a nice day, keep the door to the RV open, and leave the fan on the rug until all the moisture has been removed.
Sprinkle baking soda on the area infested with mold.
Let the baking soda sit for several hours, and use the handheld vacuum to remove the excess baking soda.
Repeat this process two or three times or until the mold is gone.