If I am not a Idaho resident do I need an archery permit to bow hunt turkeys?

You only need an archery permit to hunt during an archery-only season. There are no "archery-only" turkey hunts, just general and controlled hunts.   To hunt turkeys with a bow during a general season, you need 2 items:  a turkey tag and a valid nonresident license (3 license options: 1.  Hunting, 2.  Small Game Hunting, or 3.  Three-Day Nonresident Small Game Hunting).     Good luck.