You can take bus 919 (fast line) from Badaling to Yanqing Bus Station (the last stop). There are many taxies and minibuses in Yanqing county to Long qing xia. You can bargain the price with the driver. Or you can take bus no.920 to Long qing xia, but you should ask the bus driver whether the bus you will take go to Long qing xia because there are many 920 bus branch lines.

You can go back to Beijing along the same route. Good trip!