It is only a five-minute train ride from Alison Basford’s home in the South End to the Boston Opera House where the Boston Ballet Company dancer is performing in “The Nutcracker.” Still the ballerina always takes a book along for the trip. The Brooklyn native, who trained at the School of American Ballet, dances the role of Frau Silberhaus and has two solos in the second act of the holiday ballet, which runs through Dec. 30.