Fallout 76: How to get a bow
With Wastelanders DLC there is now bow inside the game that you can craft yourself. You can find the plans from both Settlers and Raiders vendors. The plan costs 275 caps.
It is said that Raiders at the beginning are hostile, while Settler aint. Personally when I visited the Raiders camp they were not hostile. Most likely I had already done some intro quest that turned Raiders neutral against me. So if Raiders are hostile to you, either do some raider quests or go to Settlers and buy bow plan from them.
Raiders can be found north of the map, where they turned crashed space station into their base. Settler can be found in south.