I think this question of "Fairness" is misguided. Hunting is not a game, it is a struggle of life and death. In such a struggle of life and death, the notion of fairness does not apply.

Let us address two cases:

1) The hunter as sportsman.

In this case, the hunter hunts for pleasure, for sport, and for accomplishment. In this case, the use of a bow may well provide a greater sense of accomplishment than a gun, because it takes more skill to kill an animal with a bow. However, this does not mean that the bow is more fair to the animal. Sport hunting can never be "fair" to the animal, because the hunter has nothing to lose, while the animal has everything to lose. That is not "fair," either with a gun or a bow.

2) The hunter as survivor.

In this case, the hunter stalks his or her prey for the purpose of survival. He or she needs the food or other raw materials from the animal, and must kill in order to survive. Here, the use of a gun would make survival much easier, because of its increased range and firepower. Once again, the question of "fairness" does not apply, because both parties (human and animal) are struggling to survive, and we can never blame either party for doing everything in its power to survive.

Conclusion: It is a confused question to ask whether bow-hunting is more fair than using a gun. Neither is fair, and neither is unfair. The concept of fairness is not relevant.