I do that a lot... wear a regular bra and a sports bra over it to keep from bouncing too much...

Though when I read your question I had a great mental picture of not only the two bras, but - in order to keep you dry, a towel stuck in between your chest sticking out the top and the bottom. I've been sitting here giggling for a minute... cause, that's something i can see myself doing.

I don't really have a moisture problem whenever I work out... no matter how much water I drink, I don't sweat much. I wonder if there's a different type of regular bra material that might be more handy, like a mesh...?