geeze .... I can tell you this ... I've made a couple dozen wood bows, maybe half a dozen tri-lams or 4 lam bows ... you can do it without a band saw ... I use a belt sander but conceivably you could get by without one ...
That is assuming you want to waste all your time and you have the lams made for you.
I don't see how you're going to get around using a belt sander if you need to prepare bamboo, doing it by hand would be the definition of tedious.
A band saw is nice, but I live in an apt and have no place for one. I use an electric hand plane to remove bulk material from the sides of the limbs, then I use a belt sander for finishing the sides of the limbs, some shaping of the riser, and also most of the tillering.
After that it's hand tools, mainly a half round file, a half round rasp, a coping saw for cutting sight windows and radii which are smaller than the belt sander roller, and lots of sandpaper.
I'f you've got the money and the space, get a decent band saw an a good belt sander .... don't skimp ... you need some power in both tools.
I started with a real cheepo belt sander and literally destroyed it in less than a year with heavy sanding.