Tell us more and we can help more. Depending on what bugs you are talking about, you don't necessarily need to get rid of them.
If it is a destructive pest, present in big enough numbers to be really harmful, then as noted we can probably help you figure out a way to deal with it organically, that is not harmful to the environment and to all the beneficial insects you want to keep around.
Definition of organic gardening: the practice of gardening so as to increase the health, structure and life (micro and macro) of the soil and enhance the production and health of developing plants, without using synthethic commercial fertilizers, pesticides, or fungicides.
So if your "dust" is (as I presume) a synthetic insecticide, it is not organic and if you use it you are not gardening organically.