Cymbidium White Pest Infestation

[denvervet]

I have a Cymbidium that got a lot of new growth on it this Spring. I have been battling with bugs since I got it. First I had these little black flies that lived in the growing medium, they could fly......got rid of them with Bayer Complete. Now when I lift the plant up to bring it to the sink to water it there are little small white fly looking creatures living in the plastic drainage plate, the plate is black and they are easy to see. I tried Bayer Complete twice, they came back, I tried dish soap mixed it the water and they seemed to be gone for a while, worked better than Bayer Complete. They just wont "stay" away, what can I do? Someone said they might be "white fly"? Any help appreciated!