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Some times a bath tub backs up to a closet near the faucet end. If this is the case look in the closet to see if there is an access panel, it would be low to the floor. If there is an access panel open it up and look inside with a flash light. If there is water it would be hard to reach unless it is right near the access. You could put a small fan by the access panel and get air moving around and under the tub. Some times there is an access panel in the ceiling under the tub, again usually in a closet in the floor below the bathroom. This would be the safest way to dry out this area. Do not try and apply heat in the area.

The best test to find mildew is to use your nose. Mildew has a strong musty smell. If there is mildew, you'd be able to smell it easily. Keep in mind that if things are still damp around the tub and the ceiling it will have a musty smell, but mildew has a completely different & strong smell. If you smell something musty, give it about a week and if you still smell it then there is a possibility that there is mildew. Like the other contributor wrote, find the access panel to your bathroom plumbing, take it off and use a flashlight to look inside. If the smell overpowers you, and if you see green or white marks then you have mildew. It's really hard to clean up but there are a number of books & articles on things that you can try to clean it up. Check on line and if you can't find anything good, go to home depot or Lowe's and see if you can find a book on it. Good luck-