Lanie,
The book I got this info from is "Alexandra The Last Tsarina" by Carolly Ericson.
The ball evidently took place the same evening as an event at the Mariinsky Theater ( home of the famous ballet) in St, Petersburg. After an event there, they proceeded to a ball where Alexandra became ill and left, leaving her 2 daughters behind. Evidently, this was during Tercentenary celebrations, so this would have been in 1913.
Very good book about Alexandra.