Water in which one bathes.
Bathwater can be contained in a variety of containers, so long as they are containers from which one bathes. Big steel or wooden washtubs before the iron stove, pitchers in basins on the crochet-topped dresser, monstrous porcelain tubs perched on clawed gilt toes, injection-molded plastic in the modern bath/shower combination, or my personal favorite, "wash{ing} out of a teacup in front of the fireplace", and thank you Robin McKinley.
However, I would think that few people in modern housing voluntarily take that option. The bathwater is then generally found in the tub, in the bathroom.
Before it enters the tub, while in the pipes in the street, in the water heater in your basement, water is just water. Only the specific usage makes it bathwater. So you plug the drain and turn on the tap.
Most bathtub faucets run straight into the tub, or have a combination deal by means of which the water can be switched from full faucet to shower position. If you have our bathtub, you only have a shower hookup and must fill the bath from a combination of shower water and teapotsful of hot water from the sink. This takes a while, but is not such a terrible thing; you can lie down in the tub and let the water run on the upturned soles of your feet while the tub fills. If you are Yosemite Sam or Porky Pig, in the old Warner Bros. cartoons, you fill the bath with teapotsful of boiling water from the stove itself. Then you are thwarted into ice cube status when Bugs decides the water is too hot for you, and shovels snow in through the window.
Bathwater is normally hot, for maximum cleanliness plus relaxation. Hot water both opens the pores and relaxes the muscles; yay hot baths! Cool baths have their uses as well, however. Summer, for instance, often absolutely necessitates cool bathwater. And things like rashes and chicken pox like cool water (Aveeno optional) just fine.
At first the bathwater is clear, maybe slightly tinged with chlorinate green. If you are into bubble baths, you add some fizzy business to the running water, and watch it foam. If you are into bath bombs, you throw one in. At this point the water may take on a variety of soft colors and scents. If you just want a regular bath, you do nothing to the running water at all. It maybe gets a little greener as it deepens.
You get into the bath, displacing the water. Soap and scabs and dirt flake gradually off. The water turns greyer; the steam is dissipating. The water gets into your skin. And there you are, soaking everything out of yourself.
Eureka; you have found it.