You definitely don't want water leaking inside your walls because it will promote the growth of mold which can affect the health of your family members. It doesn't take very long for mold to grow, and once it is there, it is very hard to get rid of completely. I was recently exposed to some black mold while I was remodeling my bathroom and I ended up getting extremely ill from it.
Your best bet would be to open up the wall behind the tub and the ceiling below to gain full access to the plumbing. Without being able to inspect the plumbing, you would only be guessing where the leak was.
In this kind of situation, it would be best to replace the entire drain assembly right back to the tub trap. That is the only way that you could guarantee that the source of the leak has been fixed. This would also be a good time to inspect the rest of the plumbing inside the wall. There could possibly be more leaks there that you are unaware of.