Since you are wanting to run some custom CSS 3D transformations client side, I do not see any reason as to why this would not be possible.
What would want to do is add in a HTML element on your bubble page and add in any CSS 3D transforms, divs etc to that element.
A much more elegant way to do the above would be to use (or make) a Bubble plugin.
First I exported my HTML, CSS, and JS files from CodePen. Then, I uploaded these files to a free hosting site (i used 000webhost). Lastly, I executed the html page on there and copy/pasted the URL to a HTML element on my bubble page. I made the HTML element an iFrame.
This resulted in being able to use CSS3d in Bubble.is