I had been wondering the same thing about reflected light since I will be setting up a bathroom as a darkroom as well.
I'm assuming the mirror would cause problems with any stray light coming from the enlarger, but also wonder if the enlarger should be shielded in general. There are a lot of non-black surfaces in a bathroom, and some stray light could bounce off a wall or cabinet and create fog.
My thought is to cover the mirror and to get a large piece of cardboard box to make a foldable "wall" or baffle on three sides of the enlarger; painting the cardboard matt black.
Also, be very sure the doors alone block enough light. You only need a little bit to mess things up - and you may not notice that little bit unless you sit in the darkened room for 15-20 minutes so your eyes adjust. I'll be using some black-out plastic to makes sure no light gets through the cracks in the doors.