We talked with the neighbors and actually convinced them to grow the bamboo on their side of the fence (after all, they wanted privacy too). Since bamboo can be grown in narrow strips it wasn't that big a deal, but still nice to have it a bit further away. Keep in mind when planting bamboo in the ground, that if you buy the wrong kind the roots send runners out and you'll find bits of bamboo taking over every corner of your garden. That's why it's important to buy 'clumping bamboo'.
As an additional precaution, I've always planted bamboo in containers in the ground; for instance you dig a hole deep enough for a trash can to fit into and then you plant the bamboo into that. The container acts as a barrier for the root system and you don't have to worry about bamboo popping up everywhere. Generally bamboo is fast growing and depending on the kind you buy can get really tall--the one we planted gets to be 20-30 feet high.
But you don't need a garden to use bamboo for privacy. Used in containers you could create a screen on a balcony, a deck or even in a window box for a window that looks directly into someone else's apartment. It provides shade, some extra oxygen and something pretty to look at.
Image via lifebegreen.