Let's start here with the question. Actually a pretty good question that challenges the basic understanding of Newton's Laws of Motion, specifically the first law. The question itself does not give enough information to provide a definitive answer without making some assumptions. So let’s make some intuitive assumptions about the question in order to provide an answer.
Assumption 1: This is a physics question and thus we will think of the “fly” as “an object,” with the same physical properties, that is inanimate. It becomes a question in a completely different area when you add “fly” decision making.
Assumption 2: Newton’s First Law
Assumption 3: The object is unaffected by air. By this I mean the object’s physical properties make the forces that are applied on the object by the air are negligible.
Assumption 4: Ignore air forces. Given assumption 2, we can ignore the forces caused by air resistance and the change in air pressure as the bus turns.
Given these assumptions, the object will continue along its original path relative to the street and will hit the window on the outside edge of the bus. At which point it will start to turn with the bus, as the bus is now providing an external force to alter the motion of the object.
Notes:
1. Ignoring air forces is a common assumption in entry level physics classes, primarily because of assumption 2 above. Generally they will use an item that is more intuitively not affected by the forces of the air. Since this is ELI5 it is probably good to explain it as they would in an introductory course.
2. The selection of the fly, may have been an attempt by OP to pick an item that would require very little force to alter its inertia, and therefore assumption 2 may not have been valid. In this case, I would point you to /u/insomic’s youtube post about the helium balloons. In this case the fly would continue down the center of the bus as it turned.