Identify the three classic encapsulated pathogens, and the odd one out becomes the answer.
A polysaccharide capsule helps bacteria escape being engulfed by phagocytes, which is why capsulated organisms are so invasive. Three of the listed bacteria are textbook capsulated pathogens. $Neisseria$ $meningitidis$ relies on its capsule for virulence and uses it for serogrouping and vaccine design. $Streptococcus$ $pneumoniae$ depends on its capsule as its main virulence factor, the basis of its polysaccharide vaccines. $Haemophilus$ $influenzae$ type b is invasive because of its PRP polysaccharide capsule, which the Hib vaccine targets.
That leaves $Bordetella$ $pertussis$. Its disease-causing power comes from a battery of toxins and surface adhesins, including pertussis toxin, filamentous haemagglutinin, pertactin, adenylate cyclase toxin, and tracheal cytotoxin, rather than from a polysaccharide capsule. So a capsule plays no meaningful part in its infectivity.
Hence the answer is Bordetella pertussis.
\[\boxed{\text{Bordetella pertussis}}\]