Yes, bamboo is certainly a renewable resource. A renewable resource is one that does not run out when you use it -- more of it can be created. Bamboo is a renewable resource because it is a plant and more of it can be grown as long as there is the right kind of habitat available.
Bamboo is most famous for the fact that it is the only food that giant pandas will eat. It is also well-known that bamboo is really a grass and not a tree. It has been used in Asia for a lot of building purposes because it is very strong but also very light (it's hollow).
In answering this question, I would begin by saying that a natural resource that can be in repeatedly grown and harvested is considered to be renewable. I would, however, ask further questions about the sustainability of bamboo cultivation, bamboo trade, and recycling. The purpose of such a line of inquiry would be to find out what impacts the exploitation of bamboo has on the land upon which it is grown, the human settlements that cultivate it, the traders that buy and sell it, the consumers, and the environment. It is also important to know who benefits the most in the monetary flow generated by the trading cycle of bamboo, and who is most marginalized by it. In other words, identifying the settlements that cultivate bamboo, the trade networks that distribute it, the end consumers that buy it, and any evidence regarding the effects of the disposal of bamboo on the environment, would be very useful in determining whether or not bamboo is truly a renewable source, not only from the traditional definition, but from a greater, socio-environmental one. A broader question could read as follows: Is bamboo a renewable and recyclable resource that does not exhaust itself, the land or the human settlements that grow it?