I have turned some knitting needles for my daughter who suggested bamboo or beech. I was given a bamboo floor board which was just thick enough for turning a number 5 needle which was the maximum size using my method. The headstock through hole was my limiting factor. I used a K10 with the Internal jaw set. (any jaws that close small enough would do).
Cut a strip of the bamboo small enough to go through the headstock through hole with about 1 inch protruding the chuck. This was turned to the size of needle required. I drilled a hole in a piece of wood (Pen blank section) to be the sizing tool for the needle. Used the skew to do the turning and sanded as I went along. (Similar to the stem of a goblet). If the finished end of the needle vibrates, I turned a MT2 sized piece of wood with a hole drilled in the centre just bigger than the needle and used the tailstock to support the turned end of the needle. It worked surprisingly well but I don't think I could make a living doing it.