How to clean the travertine tiles?

hi there

We just got a new home with Travertine tiles on the floor, and above the tub going to the ceiling. We want to clean it, but really have no clue what to use on it ! I have been reading on line that we cannot use bleach products on the tiles which would elminate about 90% of the bathroom cleaning products on the market. Please provide any suggestions you may have on how to clean our tiles.

Additionally, the stone is polished.

 

thanks

Chris