This is a good interpretation. Although, I need to mention that this person is already walking in righteousness and holiness, and purity, at least in regard to the possible trigger or situation the dream is about, seeing that this dream was not about a bath. He was using a faucet to wash only his hands. This and the fact that absolutely everything in the room was perfectly pure, it speaks of this person keeping himself pure and holy and righteous. There was no dirt on his hands or any other dirty objects in the room, so this person is making sure he is in the will of God.
Anyway, well done.