How do I clean the grout between the tiles in my bathroom floor?

Use bleach, half and half with water.

Use Tilex

If still not to your specs, paint it! You can get grout paint in several colors and white at your home store. I painted the grout between the ceramic tiles on the floor all over the house-lots of tile, easy, fast, cheap, tedious-but well worth it. I had picked a lighter beige and then made it darker. You can seal it also-same method-small brush, toothbrush.

Depending how bad the grout is will dictate the cleaner to use. There are several at the Home center stores which will work. Home products include white vinegar and soda mixture, bleach at a 3% dilution and ammonia at a 4% mixture. I recommend the products at your local home center. If the grout is crumbling or breaking out, I would suggest using a grout removal tool and remove all loose grout, score the firm grout to almost the substrate, then re grout. Once the job is complete then seal the grout. This will keep the grout fairly clean. The reason grout becomes dirty is soap film which clings to the surface and creates mildew which looks dirty. The sealer will keep this from adhering real hard.

Is the grout white? If so, The best thing you can use is softscrub with bleach. use a wet sponge mop and apply it over the bathroom floor, and then allow it to sit for about 20-30 minutes. Then mop back over it with a clean mop, and the grout should be white as snow.

hope this helps

Todd