The reason anthrax takes several days is that it takes the bacilli that long to produce the toxin that eventually kills the victim. But what if one exposes people not to the bacilli -- or at least not just to the bacilli -- but to the toxin itself?
Inhalational anthrax generally occurs after an incubation period of 1 to 6 days (14).
Brachman PS, Friedlander AM. Anthrax. In: Plotkin & Mortimer, editors. Vaccines. Philadelphia (PA): W.B. Saunders; 1994. p. 730
cited at Clinical and Epidemiologic Principles of Anthrax [CDC]