Is there direct bus from Meilan Airport to Qionghai Bus Station?

I am afraid not. But you can take a bullet train to Qionghai from Meilan Station near Gate B, Departure Hall, 2F; near Gate B, Arrival Hall, 1F. The trip takes about 40 minutes. The first class seat costs CNY 35.5, and the second class seat costs CNY 28.5. Upon arrival, take a taxi to Qionghai Bus Station for about CNY 10. :)