Are you thinking of a composite bow or a self bow?
I think your first step is to get a copy of two books, "Tut'ankhamun's Tomb Series, III, Composite Bows from the Tomb of Tutankhamun," by W. McLeod, Griffin Institute, Oxford, and "IV, Self Bows and Other Archery Tackle from the Tomb of Tut'ankhamum."
I hope to make a self bow later, as those are really very cool looking, with sweeping curves toward the archer, kind of strange designs. McLeod talks about construction fo the bows, what tools were available to the ancient bowyers, and there are tons of photos of all the bows, arrows, other gear, precise dimensions and measurments of each bow, all catalogued by Carter and photographed by him during the excavation. Also, strings and possible arrow quivers and cases, too. There are cross sections so you can see exactly what kind of laminations were used in the composite bows, and illustrations of nocks, quite a few varieties. Some of the photos are of how the bows were found in-situ in the tomb when they excavated. Some bows were guilded with gold leave and had intricate decorations, really beautiful work. Some were also unfinisehd bows, and he goes into the exact condition of those bows, too.
I got my copies from an online rare book dealer, they are long out of print, but worth the money just as a reference. The measurements are so precise, there is no guesswork if you wanted to make any of the bows in the books.
Dane