Is there a direct bus from Swissotel Beijing to the Forbidden City or Tianmen Square?

Yes, there are direct buses, but you need to walk for a while. From the hotel, walk about 0.6 miles to Chaoyang Mennei Station to take the bus No. 109 to Gugong (Forbidden City) directly.

To Tian’anmen Square, you need walk about 400 yards to Dongsishi Tiaoqiao South Station to take the bus Te (特) 2 to Qianmen East Station. Then walk about 0.6 miles to the square. BTW, after have a stroll at the square, you can walk to the Forbidden City.