The bacterium (Clostridium botulinum) that causes botulism is:
An obligate anaerobe
Organisms that grow in the complete absence of oxygen are called as obligate anaerobes.
Clostridium botulinum and methane-producing archaea (methanogens) are common examples of obligate anaerobes.
Facultative anaerobes (or facultative aerobes) are organisms that can switch between aerobic and anaerobic types of metabolism.
Obligate aerobes are organisms that need oxygen to survive and proliferate.