You don't pass down Hidden Abilities with an item. There is simply a chance of the offspring inheriting the HA from the parents.
Starting in Black and White, female Pokémon with Hidden Abilities have a 60% chance of passing on the Hidden Ability to their offspring when bred with a male Pokémon from the same Egg Group. In Generation VI, this was extended so that male and genderless Pokémon with a Hidden Ability can also pass it down if they are bred with Ditto. The chance of the offspring having either non-Hidden Ability is 20% each.
Starting in Black 2 and White 2, there is an 80% chance that the Ability slot of the female will be passed to the baby when bred with a male Pokémon from the same Egg Group. Starting in Generation VI, this chance is generically applied to any non-Ditto parent.