The Alexander Longbow is provided for free at the Weapons Store located at any outpost in Silver Ridge Peaks
Also, three different types of Broadhead Traditional Arrows are also unlocked and available for purchase with in game credits.
Buy the 700 Grain Broadhead Traditional Arrows in bundles of 10. Then, head out to almost any open plain in the reserve.
Plains Bison are plentiful during the day. Furthermore, they are fairly easy to get close to for a shot. Run around until you hear one of their calls, or until you spot them near a lake. As long as you stay downwind from them, it is usually not a problem to get close to them just by moving in the crouch position and avoiding loud bushes.
I recommend getting within 30 meters. After that, aim for the lungs, which are huge on this animal. The arrow tip is in the center of the screen, so aiming is reliable at close range. A broadside shot just behind the shoulder works well. If they are facing you, aim at the midline just below the chin. Even when I have taken to shooting one running away from behind, that arrow can usually penetrate forward to the lungs.
The 700 Gr arrow is a monster when it comes to bringing the bison down. If you get the vital organ hit blood spot, it will usually fall very quickly. Even with a medium size blood spot, it should only be a short chase. Remember, the achievement requires a single shot only.