How could a mosquito fly in mid air in a moving bus?

assume that the bus is already driving at constant speed, no
acceleration or deceleration.
The reason why a mosquito can fly inside a moving bus is, that you have a closed
system. Everything in this bus is moving at the same speed including the air,
every single molecule. This means all air molecules move with the same speed as
the bus. So a mosquito flying inside the bus only has to deal with movements
relative to the surrounding air inside the bus.

During acceleration or deceleration this is much more difficult. The mosquito
probably would not be able to stay on its course - similarly to a passenger in a
train, who tries to stand still while the train starts moving or while it is
stopping.

Also things change dramatically if the bus becomes an open system. Take out the
front windshield and your mosquito will not fly anymore.

By the way, we also can see our earth as the bus we are all sitting in. Earth has
a distance from the sun of about 150 million kilometers and moves around the sun
within one year. To do so the earth must have an average speed of more than
100000 kilometers per hour (76000 miles per hour). Still we can walk, drive, sit
.... because we experience our earth as closed reference system.