Is it possible to buy tickets for changsha airport shuttle bus at the CACC Aviation Hotel?

Most info online is how to buy tickets FROM the airport to get into CS city but there's no information for someone who is already in CS and wants to head to the airport--how they can buy the ticket.

Can I buy tickets at the CACC (民航大酒店) so I can catch the airport bus shuttle to go TO the airport?
If not, what are the other locations I can buy the airport shuttle bus tickets.