PEK shuttle bus to forbidden city

No direct bus is available, but you can take Airport Express and transfer to Subway Line 2 at Dongzhimen, and then transfer to line 1 at Jianguomen. After that, get off at Tian’anmen East and leave from Exit A. Walk north through Tian’anmen Squar, you will get there. It takes about 1h 20 minutes.

Also you may meet the morning rush hours, so it may be very crowded.