The answer to 'why is my bathtub rusty water' is that the rusty water is likely caused by corrosion or mineral buildup in your plumbing system. This can happen over time as the metal pipes and fittings in your home's plumbing degrade, especially if you have older metal pipes. The rust and minerals can then get flushed out when you turn on the taps, leading to that distinctive reddish-brown color in your bathtub.
Some common causes of rusty water include corroded iron or steel pipes, galvanized pipes, and even copper pipes that have reacted with certain minerals in the water. This is a common issue, especially in older homes. While it's not necessarily dangerous to bathe in, the rusty water can stain your tub and clothes, and may also have an unpleasant metallic taste or odor.