Look for aphids.

Yes, it could be an aphid infestation as the sticky residue is what is left behind as they suck the juices from the plant. Often accompanied with this is lots of ants, as they harvest the sticky stuff. Eventually though it will turn into a mold called black sooty mold.

Whenever I have an infestation like this I use Bayer Advanced Tree&Shrub Pest Control. Comes in a blue bottle for about $20 at your local major retail center. Works great, and not just for bamboo!