Yep, you can! If the smell of bleach bothers you, or you want a less harsh chemical, vinegar and hydrogen peroxide (or even just baking soda and water) can work as well. Just be warned that substituting the bleach for something else will probably mean a lot more elbow grease for you. If you want to substitute hydrogen peroxide or plain water in for the bleach, you can use the same amounts that the recipe calls for. If you want to use vinegar, a spray solution of 1 part vinegar to 1 part water is great for regular cleaning of your grout, but probably isn't strong enough to completely whiten really dingy grout.