There was a fellow at a few of the shoots several years ago who could take a stave to shootable bow with a hatchet in less than an hour, not a great, finished bow but a shooter.
You can make a bow with a pocket knife if you take the time but if you plan to make more than one or two bows I suggest buying a few better tools.
I see $10 draw knives at the local flea market pretty often, not in great shape(rusty) but usable, same for files and rasps, they usually can be had for around $2 each.