I will live in Dorsett Regency in Jianghab road in Wuhan, I would like go to Zhangjiajie. How?

To Zhangjiejie, there are only two methods, by bus or by train.
There is only one direct train K967/K966 at 23:57 from Wuchang Railway Station and from your hotel, it is suggested to take taxi to that railway station directy at night.
Or you can take direct buses from Jinjiadun Bus Station and the buses are at 09:50 and 18:50, or from Fujiapo Long Distance Bus Station at around 16:50, or from Hongji Bus Station at 17:00. The closest bus station is the Jinjiadun Bus Station and you can take local subway to reach Hanzhou Railway Station and walk to that bus station.
Or you can take the bullet train from WH to Changsha South Railway Station. Then take a taxi to Changsha West Bus Station to take the direct buses for Zhangjiajie.

I think you can choose either of them to travel.