Why A Bus Travelling At 60miles An Hour Overtakes A Car Travelling At The Same Speed?

Two vehicles traveling at the same speed in the same direction will maintain the same relative distance forever. The bus can only overtake the car if the distance traveled is shorter for the bus--for example, the bus takes the inside of the curve while the car takes the outside, or the bus takes a different (shorter) route.

The indicated speed of the two vehicles may be the same, but the actual speed may be different. That's a speed measurement problem. The fact that you can't actually measure (or control) the speed precisely doesn't alter the math or physics of your question.