Concerning the Vizard, there are special rules that are based on only them. These certain individuals have some limitations, considering the fact that they have all the powers of a Shinigami, and they get a hollow mask, etc, to boot. They must train a certain amount of posts and get a certain amount of points to be able to get Bankai. They must first reach 200 points, and when they reach that, they must complete a training amount of 2k words.
This also goes for non-captain leveled shinigami. 200 points and a 2k training topic for their bankai. This specifically includes lieutenant level shinigami. Any shinigami below lieutenant level may not have bankai. There are no Ikkakus, and if you're below lieutenant level, you obviously don't have enough power to gain such an ability.
Only the three ex-captain level vizard may have bankai automatically.