Hi Scott,
There's a brand new feature on Shapes and Buttons called "Shrink Text to Fit" (see the properties for those two objects). Would that help? That's sort of the inverse of what you want - reduce the text to fit a specified shape, as opposed to grow the shape to the fit the text.
I think all you can do at the moment is to use a scrolling text field to house the learner's text, or start checking to see how many characters the learner has typed in and show different sized shapes based on the how much text there is (0-100 chars = Shape 1; 101-200 chars = Shape 2, etc). You might have to change your whole layout of objects based on the amount of text, too (chats that have come before). I don't know how you'd deal with an unlimited amount of text, either. Usually we use scrolling text for that sort of thing. Chat interfaces are pretty dynamic!
Another new feature is to set the size the height (or width) of a Text or RichText object. Depending on the shape of your chat bubble, you might be able to use that. You would need to count characters and make a guess at the size, though.
See attached screenshot. The red "length" block is found under Advanced > Text. Hope one of those helps!