The Effort Will Be Worth It
The conditions in a bathroom can discolor your tiles and grouting with mold and mildew. How do you start to get rid of this? It may take you some time, but the effect will undoubtedly be worth it. Get your old toothbrush and some white vinegar.
Dip your toothbrush into the vinegar and scrub the tiles and the grouting. It may require quite a bit of elbow grease, so divide the room into sections and do a bit each day or if you have a partner willing to help, delegate some of the work to them.