How do I book a bus to Qingdao from Beijing, I am looking at going in the evening if that is possible for the Tomb Sweeping festival.

You can go to the Yongdingmen Bus Station to buy ticket at least one day before. To be honest, it is not suggested to take bus. The bus ticket is hard to book for you online and the bus takes long time than bullet trains.

As far as I know, there are bullet trains between the two places and they take around five hours to five and a half hours.