Quick answer: Brown bath water is rust, sediment, or minerals stirred up somewhere between the source and your tub, and the pattern tells you exactly where it's coming from. Brown only in hot water? It's your water heater. Brown from every tap? It's your pipes, the city main, or recent hydrant flushing. Clears after a few minutes? It's trapped sediment in an unused line. It's rarely dangerous to bathe in, but never drink it, and if little ones share the tub, a bath filter catches the rust and sediment right at the faucet while you fix the source.