In Denmark back in the days, they used the hollow bones in the legs, from just about any animal hunted for food. In my opinion, roe or red deer seem to work very fine.
Processing is relatively easy, as you more or less only has to give the bone a good smack on the end, with something sturdy and unflexible at the other end, to produce the rawlings.
Any further processing is mainly carving the needle round (-ish, since the needles found actually aren't completely round, much more like a standard cutting needle of today)
And drilling a threadinghole with a spoondrill of the right size, i would carve the threadinghole afterwards, to make the hole long and "flat" like we see it today on metal needles. It is my believe that they did that back in the days aswell.
And as Xylaria has written, water can help, especially on the dust. (Yes, i use Dremel aswell as large machinery, and the dust is nasty over a long period of time. I like the smell though, don't know why )