Easy enough to do by manually drawing a mask on the background layer which matches the outline of the speech bubble.
Where I'm coming unstuck is scaling the mask to match the scaling up from zero of the speech bubble. I've tried track matting and a couple of other things, but no joy yet. I'm sure this easy as hell if you know what you're doing, but like I say, I'm a little rusty!
Create Speech Bubble as solid and animate. Duplicate layer and use as track matte for the Background layer, comped on top of Speech Bubble. Use Matte Choker to shrink the Background to reveal the outline of the Speech Bubble (you may have to precompose the Track matte layer and background and apply Matte Choker on the precomp).