How did the Satan bug Kill?

This is a good question and exposes a fundamental flaw of the story.
The title of the film hints at the threat being a biological agent and an active virus and merely exposing it to the atmosphere is enough to end the human race. But this doesn't make any sense because the speed at which the virus is portrayed as killing people would not give it time to be transmitted between them. The threat would simply burn itself out.

The way the threat is portrayed is more like a chemical agent or nerve gas. But as with all chemical weapons they have to be actively dispersed in the air over a wide area in order to be effective. And once used they break down in the environment and are no longer a threat.

I think the story is very firmly in the realm of science fiction and the writer has blended the lethal threats of both a biological and chemical weapon.

However, the effects of weaponised Anthrax do bear a similarity to those in the film and reminded me of the Sverdlovsk anthrax leak. But that happened in 1979 so couldn't have been an influence for this film made in 1965.