If you can find Bambusa multiplex, it makes great arrows. The internodes are 12" apart so only 2 nodes per shaft. The culms are round with very little sulcus, thick walls and a small center hole. It's a clumping type bamboo so it isn't invasive. The clumps get to about 8' in diameter but that's over a long period of time. The culms grow to about 15' long and the shaft will come from the upper portion of the culm. The culms also make great cane poles and would probably work well for split bamboo fishing rods.
This Bambusa only grows in warmer climates.
Any shoot type shrubs will make arrows, some good and some better so go out and look to see what you can find. Yaupon holly or other shrub type hollies, maybe