From Diablo Wiki
Bow skills are all Demon Hunter skills that require or only function with a bow or crossbow or hand crossbow equipped. This is not an official designation in the game, but it is made immediately obvious when a player tries to use a bow skill without a ranged weapon equipped.
Though the Demon Hunter is meant to be the game's archer class, there are some effective attack skills that do not require a bow equipped. Most of the general purpose DH skills, buffs and debuffs and the like, function with any (or no) weapon equipped. It is possible, yet somewhat costy, to make a demon hunter based off of sword-and-board, and not use any bows that is effective in endgame.
Demon Hunter Bow Skills
The following skills require a bow/xbow/hand xbow to be equipped to use them.
Fittingly, all the skills in the Archery category do require a bow weapon to use.
Demon Hunter Non-Bow Skills
Many Demon Hunter skills do not require a bow, including most of the class's debuffs and buffs. Many of the bow skills include a debuff effect in them, such as Entangling Shot, but those skills only debuff (slow, stun, etc) the target or targets. The non-bow debuffs function more generally.