I'd recommend going to a vendor that accepts Alliance Points...
What they said. Or meet a guy named Jose on the corner, he will be wearing a yellow raincoat. He will take you to the secret hall of the bows where you can sacrifice your AP to cluckster, the roman god lf fried chicken. If he accepts your offering you will be graced with the egg of destiny. You must then take the egg to top floor of the tallest building within 2 miles and throw it off. If the egg hatches then you will be granted the right to buy a bow.
TL;DR
Have someone craft a bow for you, they are better.