Do genetics play a role in the severity someone may experience a bacterial infection?

Yes: Genetics definitely play a role in people's immune system response. Genetics also play a role sometimes in physical characteristics that make people more or less susceptible to certain infections (small eustachian tubes for example would make you more susceptible to ear infections). However, the resopnse is multifactorial and probably not all due to genetic influence.

Yes: They do, some people are more prone to certain infections based on their genes, this is a very young field in medicine so i cannot elaborate more, but the short answer is yes.