As a retired AF Member, congratulations on Basic. Ya still have to get through tech school though. My suggestion for trying to continue to build while on the base is to first find out if they have an archery range or even a Rod and Gun club. Chances are going to be pretty good you can build a bow there. If this is not feasible, I would check into finding a local archery club, preferably traditional, or even a traditional muzzleloader club that has there own outdoor range/facility. There is a good chance you can build a bow there.
I still work for the Air Force and am aware of the rules for what is considered a weapon and what /where they have to be kept and stored. They changed the requirement to include all of base housing, not just the dorms, and anyone coming onto the base. Yeah, you will not be able to store a bow and arrows in the dormitory. It will be stored in the armory. You will have to arrange to sign it in and out. If you decide to get a hatchet to work on bows, you can't store it there. It again goes to the armory. I doubt there would be a problem with storing a drawknife, because it is not listed as a weapon but you will still have to ask. You will need to get the document each base has regarding weapons storage, transportation and use. As it has been said before always personally verify everything.
Below are excerpts taken from the Offutt AFB Privately Owned Weapons document to give you an idea of what to expect:
Prohibited Items:
Any dagger, dirk, switchblade, butterfly knife, stiletto, or any other unusually dangerous instrument capable
of inflicting cutting, stabbing, or tearing wounds is prohibited. Knives with blades that exceed three and
one-half inches are illegal to carry on or about your person unless actively engaged in fishing or hunting
activities.
Trransportation of weapons on the installation:
Unusually dangerous weapons usage (i.e., bow/arrow) is prohibited on base with the exception of sanctioned
base events and the archery range.
