There is a legal definition in my Webster's dictionary: "1. the district within which a bailie or bailiff has jurisdiction." --- I wouldn't look up "bailie"or "bailiff" unless you plan on practicing law in an English speaking country. My interest as a tutor is in definition 2. "a person's area of skill, knowledge, authority, or work".
For example, "My bailiwick is English as a Second Language, if I can be of any service."
"As Jim has mentioned, my bailiwick is law firm libraries, as opposed to academic libraries."