Although bacteria can be seen without staining, not all of their characteristics can be visible. Thus, with staining one can see if the bacteria is gram positive or negative, the outer wall's or capsule's structure, the exact size and texture of the surface etc. Without staining, it would be very difficult if not impossible to differentiate between different bacteria types.
Fixing a bacteria allows the scientist to immobilize and preserve it. Thus a complex study can be performed over a longer period of time. The bacteria can also be preserved in order to be restudied at a later date.