I will arrive late at night in Wuhan Tianhe Airport and need to get to my hotel in Wuchang district.

Don't worry. You can still take the airport shuttle bus Wuchang Line and arrive at Fujiapo Bus Station. The operating hours of this bus route are from 09:00 to the arrival of the last flight. So don't worry. It takes around 90 mins. And the ticket fare is CNY 32 per person.
If you wanna take a taxi from the airport to Fujiapo Bus Station, it would cost CNY 110-120 at night.
You can choose the way you like. :)