***** Spoiler Spoiler *****
You can find the bow during the quest where ebron chief asks you to clear bandits in the forest. On East side of village there is a Forest , head further East , There will be a couple of bandits near a camp fire, beat them & loot the place. Then head further East & you can see their Camp , sneak to the backside , this will trigger an animation where part members surround & attack the bandits . Make sure that you loot everything , even the tents , most of them will say "nothing interesting" but one of them has a bunch of potions. After Finishing this Quest you must have also completed mirel's bow quest as well.
If your problem is related to some bugs ,
I got Nothin.