How to go from Changsha Airport to Changsha Railway Station late at night (12.00 midnight)?

I arrive in Changsha Airport in May 2016 at 22.30 and want to take 03.49 Train from Changsha to Zhangjiajie. Please advise whether I will be able to take a bus or taxi from Airport to Railway Station at 12 midnight? If by taxi, will I have to pay double charge since it is midnight?