You wouldn't build a bow like that with a bamboo backing. You'll need fiberglass.
Honestly, your best bet is to purchase the instructional materials and "kit" from Binghams. $300 might seem like a lot, but that's the best way to make sure you learn how to do it and get a shootable bow. Trial and error when trying to be cheap will end up costing you more money.
Also, read as much as you can in books and on the internet.