A great mixture for cleaning your bathroom tile is this, one cup of ammonia, one cup of vinegar, and one half cup of baking soda. Use this with a gallon of hot water and scrubbing down your tile just got faster.
You can also clean your bathroom with apple vinegar (unpasteurized that you find on the farm) and rub this into and over the tile for a great shiny clean.
You can clean the caulking around your tub with a bit of toothpaste on a toothbrush rubbing briskly.
To clean grime off your bathroom tiles, whip up a solution of equal parts Epsom salt and liquid dish detergent. The salt adds friction, which helps the detergent scour away the scum.