Those were the dates of Buffalo Bill's Wild West Show - however, there is always a footnote of controversy in the history books. The show opened in Omaha, NE in 1883, traveled around the USA and in Europe over the years of operation. It went bankrupt in 1913, although it was carried on several years after the bankruptcy. Bill died in January 1917 soon after his last official show in November 1916.
Annie and Chief Sitting Bull played in the show during the same time period - they became great friends, and Sitting Bull spiritually "adapted" Annie as his daughter.