is there any bus to xian from qingdao?

Yes, there are direct long-distance buses from the Main Bus Station that can take you to Xian. The schedules are 17:00 and 18:00. It costs CNY 337 per person.
If you just have only one day in Xian, you are just adviced to stay at the city. It has many popular attractions, such as Terra Cotta Army, City Wall and Big Wild Goose Pagoda. In addition, you can find many delicious local snacks nearby Muslim Quarter area. Have a nice trip!