Mites would be on the plant - blooms and leaves - in most infestations.
If you have a magnifying glass (or just really good and young eyes
) you should be able to ID a mite infestation.
Other critters can also give one a "powdery" look I believe, like some scales.
These would then be best treated with either an insecticide (if you are into chemicals) or Neem oil if you are not. I prefer the more certain kill with pesticides. Remember, if they are "alive" you kill the adults and will have to retreat for the second generation that will come along a week of so later.
First off, tho, you need to ID what exactly you have so you know what you need to do to cure your chids.