Hi Julie
I take it you are talking about domestic bathrooms. When you say 'dirty' grout do you mean milldew or just general dirt and grime?
Bleach is not a brill option - especially in such confined areas - another thing we need to know, are you talking shower area tiles, normal wall tiles or floor tiles?
Just a quick tip - when posting a question go into as much detail as possible - more chance of getting the right kind of help.
Fox