It may have come from Bamboo but it is unlikely to now be Bamboo, indeed it could as easily be called rayon or viscose rayon. From Wikipedia:
“Modern clothing labeled as being made from bamboo is usually viscose rayon, a fiber made by dissolving the cellulose in the bamboo, and then extruding it to form fibres. This process removes the natural characteristics of bamboo fibre, rendering it identical to rayon from other cellulose sources.”
It can also be Modal or Lyocell fabric/textile, TENCEL™ is a company that also produces these fibres so sometimes you will see the fabric/textile branded as TENCEL™ Modal or TENCEL™ Lyocell if manufactured by them. It is a more closed loop system to produce these textiles but it is all related to rayon as the parent fabric just different chemicals are used in the processing of the cellulose.
The reality is that any other source of viscose, rayon, lyocell, or modal is going to feel the same, breathe the same , and look the same whether made from tree cellulose, Bamboo or any other cellulose source. Sometimes because of the nature of the feel it is called artificial silk, it can mimic cotton, linen, silk and wool.
@Gaby Underwear or garments made with Modal are typically longer lasting, Modal is made in such a way that the fibres are stronger than other rayons, they are also much stronger when wet than typical rayon fabrics. It also is happy to be tumble dried which most other rayons are not so enamored with 
