If you're in Qeynos, one of the best bows you can get at your level is available as the quest reward in a simple quest.
Go to Eldaar Wood (between Willow Woods and North Qeynos), and find the archery shop. Inside the shop you will find Gregor who will quest you to go get him 5 perfect hawk tail feathers in The Forest Ruin, (Willow Woods newbie garden). You can snare the hawks to pull them and they should be grey to you @ lvl 15. Kill 5, run back to Gregor and he'll give you some cash and his old bow!
Great quest reward and a fun half hour! Don't forget to buy some arrows before you go out hunting with your new bow. To get started, you can use tin arrows which cost about 2cp each. When you're comfortable with the bow, you can switch to iron arrows which cost about 7 cp each.
Good luck and good hunting!