This isn't quite as straightforward as that. If the attack would have caused 1 point of damage if you had used a standard attack, then the Bash should have it's intended effect. However, if the attack would not have caused damage, then the Bash should not work, either.
Let's look at edge cases:
You are using a simple club (nightstick, etc.), which is a Light Weapon (normally 2 points of damage).
Your opponent is wearing a leather jerkin (leather jacket, etc.), which is Light Armor (1 point of Armor). With a normal successful attack, you would inflict 1 point of damage. If you Bash him with your club, you do no damage, but dazes him for a round.
However, let's say he had on some brigandine armor (or an armored tactical vest); Medium Armor, protects him for 2 points. With your club, you won't be able to get through that armor (unless remarkably successful on the d20). Bashing him has just as little effect as smacking him with that club - that is, none. Unless you happen to roll high on your attack, he's just going to shrug off anything you do.
Take this one step further, and place the opponent in full Plate Armor; that's Heavy Armor, which provides 3 points of Armor protection. You, with your silly little club, won't be bothering THIS handsome knight in his shiny armor! :-)
(At least, that's how we play it...)