Which subfield would involve a political scientist who would specialize in how a bureaucracy (in any country) implements governmental policies?

The answer would be Public Administration. This an disciple where the operation of government policy and also an academic discipline that studies this application and makes civil servants for functioning in the public service. Public administration is "mainly worried with the group of administration policies and programs in addition to the behavior of administrators formally accountable for their behavior.”

From mexican american war , us gained new mexico.