In general, bamboo is unharmed by pests. Aphids and white flies are not uncommon. They appear as little tiny dots, between the size of a pin head to the tip of a pencil, as shown in the photo below.
There are a number of ways to combat these types of pests. If there are only a few, and it is practical, a blast from a hose will sometimes suffice. There are many brands of insecticidal soaps available on the market that will easily get ride of aphids and white flies. Most are organic. They only treat soft bodied insects and are harmless to hard bodied, beneficial insects such as lady bugs. If you are experiencing a major outbreak of aphids or white flies, releasing lady bugs is a great way to get rid of them. They go right to work for you (see below), are easier to apply than soaps or chemicals and are sometimes less expensive to buy.
The other type of insect that you may encounter on your bamboo is the bamboo mite. See the picture below, taken in Portland Oregon, at the Portland Zoo. The mites are underneath the leaves and inside of their nests during the winter months.
Damage is visible through the foliage. Bamboo mites are native to Japan and here in the US there is no known predator. In the event of an outbreak of mites, it is best to use a miticide. If the outbreak is limited to just a few leaves, removal of the leaves may be enough. Burning the bamboo is another choice. Although it sounds drastic, it is actually quit easy. Spring time is the only time you can do this and you should not do this to clumping types of bamboo. Just before new culms are starting to emerge, cut away all the old culms, removing them and any leaves on the ground in the surrounding area, as mites will live in bamboo leaves on the ground. Burn the canes and debris, as well as the ground area surrounding the base of the plant. You want to make sure to treat any mites that have fallen off around the plant. Afterward feed with a small amount of nitrogen fertilizer. Make sure to monitor the new culms as they emerge and remove any leaves that have signs of mites.