Why do birds that walk on the ground walk so "bumpy"? Most other animals walk quite smooth, doesn't matter if they are mammals, reptiles or insects or walk on two, four or more legs. Birds seem to be an exception and there is no difference between flying or non-flying birds.
If you mean the head bobbing displayed by many birds when walking: it is believed to help with visual stabilization.
The term head-bobbing, used for the apparent back and forth movement of the head of some birds while walking on the ground (think pigeons), is a bit of a misnomer. These birds don't actually bob their heads back and forth – instead, they move their body forward, leaving the head behind, then thrust their head forward past their body (hold, high-speed thrust!). This innate behaviour is believed to help several key aspects of vision during locomotion and foraging. While the head is still, images are stabilized on the retina and moving objects become clear against the background, and during the thrust phase, depth perception becomes more accurate.
In this article you can find an stroboscopic photography that shows the particular bumpy walk.