What can I use as a temporary noise insulation on a door that connects bedroom and bathroom?
Fill the cracks around the door, especially at the bottom with egg crate foam. Cut it up and pack it in. Preventing air movement will help a lot with preventing sound transfer. 

An alt to the foam is weather stripping. This would be a more permanent solution that will allow for the door to be used and still help to deaden the sound. Something that would would have to bug your landlord about before doing it.

Once that is done putting something solid in front of the door on the other side like a bookcase or decorative rug will help even more. If you can hang towels on the bathroom side as well that will help a little bit.