It's simple enough, really; all you need is a single, highly contagious disease that doesn't kill the victim (or manifest crippling symptoms) before they can spread it. In some ways, it's better to have a crippling rather than lethal bomb, as that could paralyze hospital services even more.
Either way, if you can produce a suitable version of a naturally occuring virus (perhaps through genetic manipulation; I'm not sure how easy it is to hide markers for that sort of thing, of course), infect a single carrier in a populated area, and just stand back you'd see an epidemic which would be virtually untraceable back to you.
Hence the fear over the potential use of weaponized variants of smallpox made by the USSR during the cold war, which are either lost or sold on the black market. Weaponized, of course, meaning that the chemical or virus (etc) is processed in a form suitable for use in killing people. Like increasing virulency, or specifically creating the dry spores required in the CBW use of Anthrax.