Just as a dry bag can accidentally succumb to abrasions and punctures, it can with mold and mildew. When this happens, you obviously want to do everything in your power to remove it. Thankfully, you can do so without needing fancy equipment or products. That is unless the mildew is too substantial. For moderate mildew and mold, start off with hand washing your bag in hot water (around 110 degrees Fahrenheit) with a sponge (being gentle if using the grit). Anything hotter than this can damage the tapes on the seams. To wash it, use a non-detergent soap. Be sure to avoid bleach and solvents as they can negatively affect the waterproofing of a dry bag.
If this does not seem to do the trick, you can also try mixing one cup of salt and one cup of lemon juice concentrate to your hot water. Either way, be sure to thoroughly rinse your dry bag to rid it of soap or the salt and lemon juice solution. To dry, do not do so in the dryer as the excess heat can damage the seam tape.