For purely bullet-resisting purposes, most helmets do not provide a lot of protection. While they may be useful for ricochets hitting at a lower velocity as well as shrapnel, a bullet fired from a rifle will easily pierce the side of any helmet, even modern ones. In the Civil War, a new type of ammunition was introduced called the Minie Ball which was especially devastating. Using the same approximate caliber size as the musket ball rifles of prior wars, the new conical ammunition would shatter bones that would have broken with the lower velocity, round musket balls.
So because there was no real advantage to wearing a helmet and because metal was in short supply during the war effort, kepi hats were worn instead.