Transpile React app to make it appear in a modal

I’ve got a (small) React app (vanilla create-react-app), that I would like to appear in a modal (bootstrap or similar) on another site. Is there a library that will simplify this process?

Specifically, the entire use case is that if my Javascript file is loaded (and just one javascript file), it will insert a “Click Me” type call to action, and when clicked my App component will be loaded into a new modal. It will need the CSS (for the app) to be included in some form as well.

I think all of this (excluding the call-to-action which is fairly simple) could be done during Babel/Webpack transpilation but I can’t find anything off-the-shelf that seems to do this.