The flight from Wuhan to Xian should not be more than $500 chiinese yuan, however, it depends on the schedule as Chinese New Year approaching. The best way to visit Terricotta Warriors is of course to join in the local tour (1 day tour)as the tour guide will explain its history. However, if you just need to go purely for sight-seeing, then you can actually take a direct bus from Xian train station. Staying at Bell Tower hotel should be better as you are view the night scenary.

Thanks Mr Mike. How early do we have to buy the air ticket? Is is possible to buy on the day we travel or does it need to to be few days in advance?

You coud purchase the air ticket on the spot; however, no discount will be enjoyed. Usually, it is suggested that you book the ticket 2~4 weeks in advance, when the discounted tickets are supplied. I think you co uld pay attention to the real-time airfare online. Here is a search tool: https://www.travelchinaguide.com/china-flights/