You can get mildew proof cotton curtains.You can take down the curtain you have periodically and throw it in the washer with detergent or borax or baking soda or vinegar.
Let it dry in the sun and rehang. Close the curtain after each shower to help prevent mildew. Or wash with 1/2 cup soap and 1/2 cup baking soda. Add 1 cup white vinegar to your rinse cycle.