Bierce and Twain were rivals. Bierce wrote for the San Francisco Enquirer (William Randolph Hurst) and was a geographic officer with Henry Thomas in Tennessee during the Civil War. His short stories reflect the arabesque and harken roots to Poe.
Bierce didn't personally care for Twain--it seems that Twain's choice to go to Nevada and abandon a career as a Mississippi river pilot during the unpleasantness of the 1860's irked Bierce's sense of morality.
Bierce was known to honor veterans of either army, considering them as kindered souls. In Bierce's opinion, Twain could never pass that muster.
BTW Bierce never died, he disappeared. After the attack on Columbus, New Mexico by Pancho Villa (1914?) Bierce talked Hurst (actually he threatened to quit) into letting him accompany Pershing into Mexico to extract revenge. Bierce split off and disappeared in into Mexico. Legend has it that Bierce found Villa (Pershing never did).