I have a shape that was made in Illustrator. See right. It's the thought-ballon-y-looking thing.
The everything outside of the black part is transparent. I want to use this shape as a mask so that another comp will appear inside the balloon shape, but not outside the shape.
Easy to do?
Use the layer as a Track Matte.
Typically, you would duplicate your bubble layer, put the new copy above your "bubble contents" layer, and set your bubble contents layer's Track Matte setting to "Alpha Matte".
If you parent the duplicate bubble layer to the original, any animation you do to the original (visible) bubble will be replicated by the matte layer.