would like to go Beijing, Xi'an, Shanghai by bullet train 11/20/14

arriving in Beijing on 11/16 from Sydney,AU. Plan to spend 3 days in
Beijing, travel to Xi'an and visit warriors & museum. Can I leave the
same day for Shanghai by bullet or will I have to go back to Beijing?
Plan to spend 3-4 days in Shanghai & bullet back to Beijing airport
hotel on 11/25 to depart 11/26 early am flight for US. Any help greatly
appreciated. (solo female senior traveler)