Please tell me what public transportation I can use from Beijing west railway station to

You can take subway line 9, get off at National Library first. Then take subway line 4 to Xizhimen Station and take line 2 to Jishuitan Station, Exit A. After arriving, walk north around 0.6 miles to find the hotel. The wholeway takes around 25 mins. And the ticket fare is CNY 4 per person.

Or you can take bus no. Special 13, get off at East Jishuitan Bridge Station. Then walk northwest around 0.6 miles.