This may not sound quite right to people but I like to trim things to fit... so my answer to this would be cut the box down the middle with half the pizza remaining in each side, stack the halves on top of each other with the open sides faceing one direction, cover the open side with foil or something and shove them in the insulated carrier. Those things are soft (as far as i can tell from seeing the pizza delivery guys with them) so you can kinda fold up the end that's not being used. Im guessing that would fit on the back of a bike strapped in with bungees. If you're worried about the squish factor, the pizza place might have a couple of those plastic peices they put in the center to keep the box from sticking to the middle fo the pizza.