The bushing barrel uses an external bushing at the muzzle end. The sides of the barrel are basically straight. The bull barrel's end "flairs out" and no bushing is used.
Extremely accurate 1911's are generally bushing type because it can be fitted precisely so the barrel locks into the frame exactly the same each cycle.
Bull barrel guns are also popular, and can be fitted very well.
I don't know how much accuracy difference there is between the basic designs, probably not a whole lot. The bull barrel design has fewer parts, is easier to take down, and has a little more weight out at the nose.
Theoretically, the bull barrel has more bearing surface, is stiffer and helps to dampen recoil and increase accuracy.
On the downside, bull barrels tend to be heavier and require that the frame be milled out for a supported ramp. Therefore, once you have a bull barrel frame, you cannot go back to a standard bushing and barrel.