I had a house with a slate roof. 90 years old and still going, last time I passed by. My present house has a black slate floor in the living room. It was protected when new with a clear coating...I think it was called Stonyl. Never stained, but that's not the problem. It's so cold and dark that we've completely covered it with carpeting. So one thing to think about is not to mass too much of it in a poorly lit space.

You might want to get a sample and test it with bleach, but not for color. I believe you'll find that some examples of finished stone become extremely slippery with a wet coat of bleach solution. This may be important if you ever want to clean your bathroom floor.