Xian City to Xianyang Airport at Night

Hello,

I'll be flying to Guǎngzhōu from XA but my flight will be early in the morning (at 7.00AM), so I need to get to the airport early. I'm trying to plan a route from my hostel Hàntāng Inn (汉唐驿) to the airport at night/midnight. I would like to ask what's my best option for this one. My starting point would be the Xīhuàmén (西华门) station.

Is it possible for me to catch up with public transport or do I need to get a taxi?