Thank you Chris. I should have put the date on my question. Her indenture papers read 1878. I did find a book on Amazon and I wouldn't mind buying it if I know there was a real chance she might be in there. She was not on the orphan trains. She was 9 years old when she was adopted. I have her indenture papers and a letter to the Mrs. Bavin who adopted her, but I don't know Mrs. Bavin's first name or their exact location. The one possibility I found in the 1880 Census, of course, doesn't tell me if she was adopted. It just has her as daughter and the age is right and approximate logical location. Katey ended up in Chenango county when she married my great grandfather so it makes sense she was adopted at least somewhat close to that area. The family story is that there were 13 children and 7 of them were put up for adoption because they couldn't afford to feed them.
The 1880 Census I found has a Catherine Bavin of the correct age in Smyrna, Chenango, New York. Her mother is a widowed Harriet Bavin (56) with three grown sons from 27 to 21. Smyrna is pretty close to Plymouth which is the address on her indenture papers. Would you consider this a pretty likely match?