You usually get your first bow from the box the Prophet gave you. Later you can harvest wood (logs on the ground) and craft a bow at a woodworking station. The starter islands (well, not so starter anymore) are filled with all sorts of resources, try there.
Don't worry about it. Just keep killing stuff - one of the mobs will drop a bow pretty soon. There are thousands of weapon drops in this game.
If you get really fussy over exactly what type of bow, you can craft one - but I really wouldn't bother.
Don't buy one off anyone - that's really a waste of gold.
'Clever' sigs get old real fast - just like this one.
What level are you? I always craft my own bow every 4 levels. On the side note, I have NOT found a single bow that is useful (useful means better than what I carry). However, my wife found lots of different staffs she can use and did not need to craft her own staff. Drop rate for bow is terribad...other weapons are good.
What Shimond says... once you exit Coldharbor, you'll reward with a package...open it and its a bow. That's the only bow I use that is not craft by myself.