Arundinaria is the only native cane in the US and it has 3 species, A. gigantia(river cane), A. tecta(switch cane) and A. appalachiana(hill cane). Of these three hill cane is the best, then switch then river cane. All three make good arrows but river cane with it's thinner walls, bigger center hole, more pronounced nodes and more pronounced sulcus(indentation above the node) it is the least desirable.IMO All other bamboos are exotics, mostly from Asia.
Arunda donax, giant reed cane can be used for arrows but like phragmites isn't very durable.
There are Asian bamboos that make good arrows too, Japanese arrow bamboo, Tonkin and others that grow in the US.