My bathroom is infested with tiny black flies
The images are too small to see any characteristics for identification. It is late in the season to see cluster flies inside so you will need to look around for a food source which might be feeding larvae of the flies. A small dead animal is possible.
I would need better images and something to give me a size reference.
Fungus gnats like moist soil where the larvae eat decaying plant material. Do you have plants in the room? If so, look closely at the soil. You might see the larvae but they are very small. The general body shape does not look like gnats.