Sort of.
When talking about movement, you need to talk about what moves relative to what. When you are standing inside the bus, you are stationary relative to the bus and moving at the same speed as the bus relative to the road. When you jump, there is no force acting on you (other than that involved in jump and gravity, both of which are vertical), so you get no acceleration in any non-vertical direction. This mans that you keep moving at the same speed relative to the bus and the road.
With earth rotation, you and still air are moving at the same speed, relative to Earth center, as Earth crust. A cloud that appears not to move is actually moving at the same* speed relative to Earth center as Earth surface.
Wind is simply air that is moving relative to Earth crust, which is due to difference in pressure, which in turn is a complex process due to differences in humidity, temperature, etc between different places. Wind, which is typically stronger at higher altitudes, moves clouds relative to you.
*Actually a bit faster since it is further from Earth center and is moving on a circle of wider radius, but difference is negligible.
You are moving, the bus is moving, just standing in the bus doesn’t see you move around. The Earth is spinning, but so is the air in the atmosphere. When you jump on the ground, the Earth doesn’t spin out from under you because you are spinning at the same rate as the Earth before you jump. It’s all the same mechanism.
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