Your toolkit is more than adequate for bamboo bows as well as stave-made. There are stave-bow builders here who don't have any more, except a drawing bench or whatever it's called to hold the bow while you work on it. I have an Indonesian friend on Java who builds excellent bamboo bows with no more. Look at bow designs from that part of the world for inspiration -- loose laminates, bundle bows, whole and split culm and more.
Stop cutting new green bamboo! You want culms that are 6-8" diameter and at least a year old but not dead. Unless you're building bundle bows... then you want 1/4" to 1/2" culms to bundle. But you still want at least year-old sticks, not new growth.