only thing you need is a hatchet and a sharp knife and you can build a bow, rather slowly! lol
or a big knife
, my favorite tool for building a bow, is a bowie, its big, sharp( IF YOU TAKE CARE OF IT), it can be used for chopping like a hatchet, and can be used like a drawknife as well(keyword is like, you can line it up, hold onto the tip and the handle and pulll back slowly for similar results,)
a good bowie will cost like $25 they arent expensive, and are a great tool in my opinion