Pokemon bank does not reset happiness, the pokemon will come out of holding in the same state that it went in, if you are withdrawing it with the same trainer.
Happiness is to do with the trainer rather than the pokemon, so if you are just putting the pokemon in the bank and then withdrawing it later, the happiness will be the same as when you put it in.
If you are putting it in the bank and then trading or transferring it to another trainer, then the pokemon's happiness will change according to the new trainer.
Pokemon bank is an application service for users of pokemon x and y.
It will allow the user to store, manage and deposit pokemon into it for a small annual fee, and is available on the internet. When a pokemon is put in the bank it will stay exactly the same until the user withdraws it.
The happiness of a pokemon (also known as friendship) is a measurement of how much it is attached to its owner and enjoys being with them. It can have different affects on certain pokemon.
I will always remember playing pokemon yellow, my first pokemon game, and being given a Pikachu. When you first got given the Pikachu, it really didn't like you and wouldn't even look at you... but as the game progressed, you developed a bond with him and it made the game a whole lot more enjoyable.