Yes, 936 bus is the best way. Walk across the road (Jianguomen Nei Dajie) from the hotel and further for about 500 meters. You will find the Beijing Railway Station of Subway line 2 nearby Henderson Yansha Department Store. Get in and take the subway line to Dongzhimen. Get out from the exit to Hanting Inn (汉庭酒店). Keep watching the road signs to show 东直门外斜街. Walk about 10 minutes to find the 936 special Tourist Line (936旅游专线). Other 936 bus will only get to Huairou, but not Mutianyu directly. So, get on the right bus. 936 special Tourist Line is not available after November 25. So, if you get there in winter, you should take other 936 bus to Huairou first and then take a shift to Mutianyu then.

Well, I also find the new timetable for Bus 936 Special Tiurist Line. It will be helpful. The bus departs from Dongzhimen at 7am and 8am and back from Mutianyu at 2pm and 4pm from Monday to Friday. In the weekends, add one bus at 9am to Mutianyu and add one bus back at 3pm.