Is "bacteria" considered an example of a foreign body?

The answer is yes. An agent is considered to be foreign if it is found outside of its normal environment. For example, if a bacterium (PL =bacteria), Pseudomonas aeruginosa is found within the blood of a human (i.e., host), it may be considered a foreign body or agent.

In an immunological viewpoint, an antigen is a foreign substance, or agent, this induces an immune response in the host. An antigen may or
may not be bacterial. The specific parts of the agent that induce the immune response are known as antigenic determinants.

References:
Tizard, Ian R., Immunology An Introduction, 4th Edition, Saunders College Publishing (1995)

Tortora, Gerard J., Microbiology, 6th Edition, Benjamin Cummings, (1997).