Try to remove as much dirt and mold as possible using natural cleaners. First, sprinkle baking soda all over the caulking.
Fill a plastic spray bottle with undiluted white vinegar. Spray the vinegar all over the baking soda, which will create a fizzy reaction that will help remove dirt from the caulking.
Scrub the vinegar and baking soda into the caulking and rinse the mixture clean with hot water.
Use bleach to clean the caulking if the baking soda and vinegar doesn't remove all of the dirt or mold. Mix 1 part of bleach with 3 parts of water in a plastic spray bottle and spray the mixture all over the caulking. Allow it to sit until it's dry.
Scrub the bleach with hot water and rinse it clean. Repeat this process weekly to keep caulking looking its best and eliminate the possibility of mold or mildew forming.