it is highly possible that the water has changed colour due to the excretion of some heavy metals, its a possibility that an addition to the bath water, some soap or shampoo along with excretion of bodily toxins and everyday dirt could cause a more severe change in colour, such as black, due to a chemical reaction.
personally i doubt that the black could be solely attributable to mercury excretion, to turn a whole bathtub full of water black in the first place with mercury alone would take alot of mercury. probably more than you could possibly contain without severe acute effects.