Bureau and agency are basically synonyms for "office". Bureau is more common in the context of a government department. An agency usually has agents working in it, not surprisingly, like a real estate agency or a law enforcement agency. Entity is a more general word, it can apply to almost any organization in business, government, education, etc.

Example: State Department: government agency State Department Bureau of Economic and Business Affairs: government bureau under an agency Entity: normally a singular person or office Sometimes bureau can be used for things like FBI - which is independently run

What you're running into here is the overlap of usages and meanings of words. Just because words overlap does not mean they are freely interchangeable. All bureaus and agencies are entities but not all entities are bureaus or agencies. So when you use a word that has broad scope (multiple meanings) you need to make it clear what meaning you intend. That can be accomplished with complement or clause within the sentence itself or with context provided by surrounding sentences.