The term "President Bush" typically refers to two different individuals who both served as Presidents of the United States.
When you use the term "President Bush," it is important to specify which one you are talking about if the context is not clear. You can say "President George H.W. Bush" for the first president and "President George W. Bush" for the second.
In discussions about U.S. history or politics, you might differentiate between their policies or leadership styles. For instance, you could say, "President George W. Bush's response to terrorism was very different from his father's approach to foreign relations."
Outside of politics, "bush" can also refer to a type of plant or shrub. However, when capitalized as "Bush," it specifically refers to the two U.S. presidents.
While there are no idioms or phrasal verbs specifically related to "President Bush," you might come across phrases like "Bush Doctrine," which refers to a specific foreign policy strategy associated with George W. Bush.
In summary, "President Bush" refers to either George H.W. Bush or his son George W. Bush, both of whom had significant roles in U.S. history.