Try using a mixture of bleach & water. I'm not sure of the ratio, but don't make it too strong. Possibly about 2ounces of bleach to a gallon of water may help. Put it in a spray bottle and spray away. Then scrub it down with regular cleaner to urge the bleach smell out of the room. You can use some commercial products if you wish, too. Just make sure they have some bleach in them. It's the best disinfectant for the job. Open your windows, and run a fan if you have one, before you spray. Also wear a mask if you have one. The bleach is very harmful to your lungs.
You can use a mixture of bleach and water, or bleach and cleaner (NOT an ammonia-based cleaner, because the fumes from mixing bleach and ammonia can cause serious illness and even death) ... But it's the bleach that kills the mildew, so why water it down or waste money on other cleaners. Just use bleach. If water has gotten underneath caulk, the only way to get rid of it is to remove the caulk, wipe down (or spray) with bleach, and make sure it is COMPLETELY dry before recaulking, or it will return quickly. You can use a fan to dry it faster, or if you have another bathroom, just let it be for 24 hours until dry. Some forums suggest using a caulk that has a mildew-inhibitor, so I would suggest that as well.