Thanks for your help - how much is a taxi to Shangri La Hotel, 29 Zizhuyuan road, Beijing

The direct taxi fare is around 110 to 120RMB.

From the airport, there is no direct shuttle bus to your hotel. But if you want to save money, you can take the airport shuttle bus line 5 to reach its terminal and then take a taxi to your hotel.
From the terminal to your hotel, there is about 8km and the taxi fare is around 25 to 30RMB. The shuttle buses can be easily found in the airport by following the direction boards.