The bayonette did change warfare, but not decisively. Before the advent of repeat-action rifles and machine guns, no manner of sophistication in weaponry meant anything on a strategical scale, and therefore organization, tactics and strategy were key (see, for instance, the result of the introduction of European style warfare in India; the British didn't conquer the place 'cause they had better guns, but because they were better organized). And after the diffusion of said technology (i.e. when everybody had machine guns) around 1900, it returned to that.

Oh, I forgot one more crucial innovation in warfare that decisively changed things worldwide: the bright European idea of putting guns on (big) ships. While it took them until the 19th century to achieve a decisive technological advantage on land, at sea Europe had been far ahead militarily since the 15th.