The ability to make a proper bow from what is found in the bush is an art that very few people still have. I would love to have such skill but realistically if it came down to it in the bush, I'd likely go the route of the snare...or a spear.
There might be another options however...
Last week my wife and I went to the provincial museum here in Edmonton which has a huge area dedicated to our aboriginal peoples. One weapon which was used by some tribes to hunt (and I forget it's proper name so forgive me) was basically a giant arrow about 3 feet long with a proportionally thick shaft. It was hurled at it's target using a throwing stick which had a very catapault like counter weight stone attached to it....apparently it was quite good at putting the hurt on buffalo. It reminded me of short spears I've seen which I think are used in Africa and also thrown with a stick to assist but these are much more sophisticated as the throwing stick is counter weighted, and the arrow has a stone head and is fletched just like a regular arrow.
I think a person could make such a contraption in the bush without too much practice...and the larger arrows would be easier to find plus harder to destroy.
Makes me want to go find a good straight stick and test it out.