elected officials by definition are not bureaucrats
Technically that is correct. But since you are known to make broad statements yourself yet split the hairs of others does that indeed apply to all of Joe Biden's almost 50 years in Washington?
The Executive Branch's Cabinet is made up of the president, vice-president and appointed, not elected, department secretaries that recommend and even make policy. That makes the cabinet a bureaucracy and since the president, and vice-president in the president's absence, head the cabinet and its policy making work they are de facto bureaucrats. A further argument could be made that Executive Orders which bypass the normal legislation process also make the president a de facto bureaucrat.
So one could make the argument that Joe Biden has been a bureaucrat while in Washington, just maybe not his entire time there.
That said, @raleighherdfan seems to be more correct than you are in context. Point to him.
Gee, what is dumber than a rube? A yokel? Or a Hoosier?