It wasn't long after the discovery of bacteria and the germ theory of disease that the use of such microbes by terrorists was suggested by H.G Wells in a short story - The Stolen Bacillus, first published in 1894.
From the Literature, Arts and Medicine database:
This story is a chilling satire about the potential role of scientists in facilitating bioterrorism. The Bacteriologist is so pleased with his own work that he gives the Anarchist access to it, and in expounding on the power of the cholera bacillus (which he feels he has in his own power), he gives the Anarchist the information he needs to recognize bioforms as an effective weapon. The Anarchist's words are all too familiar; he says that others are "blind fools to use bombs when this kind of thing is attainable"