There were no "bath rooms," royal or otherwise until the 20th century. That's why, in Europe, they're called, "W.C.," water closet. Royals and others used "chamber pots." In modern hospitals, these are called "bed pans." Servants took them and emptied them out. In "Black Lamb and Grey Falcon," Rebecca West describes how the Empress Elizabeth of Austria-Hungary, as late as 1890 in Vienna, did her business in a hallway behind a folding screen while an armed soldier stood guard in front. Of course, West describes this as a humiliation that even the Habsburgs were obliged to undergo.
While on a tour of Poland, I saw the 14th century castle of the Teutonic Knights. The "toilet" was in a tower, and "everything" ran down a trough to an opening, where it fell to the ground, hundreds of feet below.
It is a complaint of sanitation in those times that every one threw the contents of chamber pots out of windows in large cities, and the waste flowed untreated down a channel in the center of the narrow streets.
Servants would bring hot water to fill a tub. This was hard, so comes the story that Elizabeth I of England took a bath once a month, "whether she needed it or not." There were no sinks. People could get a pitcher of hot water and a bowl every morning to "wash up." In the U.S., this persisted into the 20th century. Walls and floors were not different. After all, one would have to be pretty dumb to spill something.
To get an idea of a bath tub, you have to go on-line to see a painting called, "The Assassination of Jean-Paul Marat." Marat had psoriasis, so he sat in a tub up to his neck all day. He was one of the authors of the Terror during the French revolution (1790). Charlotte Corday, upset over the Terror, traveled from Cannes to Paris, got entry to him, and stabbed him to death.