From the peninsular hotel, Beijing, how do i get to the bus stop for the direct bus to Badaling?

The fast and convenient way is to take the taxi to reach Deshengmen Station directly. The taxi fare is around 30 to 40RMB.
The cheap way is to use the subway. Your hotel is close to Dengshikou Station of subway line 5, you can walk to reach that station to take line 5 to reach Yonghegong Station where you can change to line 2 to reach Jishuitan Station. Then you can easily walk to reach Deshengmen Station.