Few different options for natural cleaners:
1.) You can always mix baking soda and water for a nice all-purpose cleaner (about 3-4 tablespoons of baking soda for 1 quart of water).
2,) You can also try a combination of white vinegar and water - works well for grease and other kitchen stains.
3,) For the bathroom, instead of bleach, try a combination of water and hydrogen peroxide (about 1/4 cup of hydrogen peroxide to a cup of water).
Hope these help!