Is there any bus going from Zhangjiajie Airport to Grand Canyon glass bridge?

There is no direct bus. I suggest you take a taxi to ZJJ Central Bus Station with CNY20 or so, where you can take a bus to Wulingyuan. Then change to another bus to Grand Canyon and walk to the glass bridge. By the way, you have to make a reservation for the glass bridge. They don't sell tickets for it on the spot.

Alternatively, I have another suggestion for the transportation, take a bus at the Central Bus Station to Jiangya Hot Spring and get off at the Grand Canyon on the way. After that, there is still a long way to the scenic area. You can transfer to the free shuttle bus of the canyon to head for the entrance.