Black (gray) hot water from tub only

I am getting sediment from my hot water supply through my tub faucet. The water has a gray appearance due to fine black sediment in the water.

My water heater is about one year old, and I am not having this problem at my bathroom nor my kitchen sink. What could be the source? What is the solution?

Can you post a pic of the water lines connected to the water heater?