Answer: Bamboo can make a great screen provided you select a hardy, adapted variety. I would strongly recommend a clumping form that will be less invasive. If you want to try a spreading type, you can install a deep, strong, vertical barrier into the soil to prevent bamboo from spreading, but that might be quite a chore on your steep slope!
You can check out the American Bamboo Society web site for info on types and characteristics of bamboo species and varieties: http://www.bamboo.org/abs/
However, I think a better alternative is to plant a row of evergreen shrubs and trees, as they will not threaten an invasion and will give superior screening during the winter.
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