I am searching for records of my grandmother and her twin sister who were in an orphanage in Burlington. In the 1900 Cencus I found several.
Providence Orphan Asylum (Sisters of Charity), St. Joseph's Orphanage & Hospital, and Home for Destitute Children. The residents are listed at E.D. 295, 64, and 72. My grandmother aged out at 15 when she was placed in a home as a servant. She was listed in the 1900 cencus under the head of household that employed her. I found her using the Soundex cards on microfilm.
Good luck!