Is there a bus shuttle from Beijing Airport to Dongying? if so where do I catch it? how much does it

From the airport, there is no shuttle bus to Dongying.

You can take the airport shuttle bus line 1 to reach Dabeiyao (Guomao Bridge) Station and then change a taxi to reach Bawangfeng Long-distance bus station, where direct buses to Dongying can be found. The bus fare to Dongying is around 151RMB per person and the buses are at 07:30, 09:00, 10:00, 11:00, 12:00, 13:00, 14:30, 16:00, 17:30 and 19:30.