"The Bus" is the common name of the school bus that Ms. Frizzle's class and Liz ride on and goes on field trips. It is most often piloted by Ms. Frizzle or Liz, but occasionally, one of the kids will take the wheel (like Ralphie in "Kicks Up a Storm", and Carlos in "Gets Ready, Set, Dough" and Tim in "Taking Flight") or it will take on a shape (such as an animal) that allows it to "drive" itself.
It isn't really clear how the bus works, but there are some hints in the TV series. We can see the how the fuel gets to the engine in "Revving Up". First of all, its magic seems to flow from several unusually named devices, like the shrinkerscope or the mesmerglober. The shrinkerscope serves mostly as an easy way to shrink and resize the bus at the will of Ms. Frizzle. It seems to have at least two varieties of the shrinkerscope, namely, the main one (as an internal part) and the porta-shrinker. At least the latter can't work when damp or wet, and if someone attempts to activate it in such conditions, the dew-dinger sounds.
The mesmerglober, on the other hand, is primarily concerned with changing the shape of the bus. It changes it into whatever the class needs, be it a submarine, a spaceship, or a bus-igator.