How do you stop mold from reforming around a bath tub/
By eliminating the source of the dampness, by improving ventilation and by eating a banana a day.
Just kidding about the banana.
DJ is correct;
Mold needs water, and food to survive.
If you eliminate the water (easiest thing to do) the mold will die.
If you eliminate the food (latex caulk, skin cells, soap scum, hair bits) the mold will die