We would like to go to Binglinsi from Langzhou tomorrow, but the way to get there and back is unclear.

You can hire a local taxi to local west bus station, where you can find buses to Liujiaxia. Upon reaching there, you can hire a local car to Liujiaxia Dam where you can find fast ferries to Binglingsi. After visiting the temple, you still need to use the same way to get back.