Today I sourced a census record for Ida D. Hancock in the 1900 census of Marion Co., IN that fits with the profile of my great grandmother. Ida was living at the "Door of Hope" mission on Alabama Street in Indianapolis. Further research on the web indicates that the "Door of Hope" was a mission and home for unwed mothers on 132 N. Alabama St.
The listing shows Ida D. Hancock, born May 1874, aged 26, widowed with 2 children living. This matches the information I have for my great-grandmother Ida. Ida was born in 1874, probably in Owen Co., IN. She married Samuel Hancock on August 27, 1892 in Monroe Co., IN and they had filed for divorce in May 1894 because she claimed he had abandoned her. In the 1898 city directory of Indianapolis, I did find Ida Davis living at 606 1/2 E. Wabash St. Ida's daughter, June, was born June 11, 1898 in Indianapolis.
So far the information fits for what I do know about Ida. I have found no other record for her in the 1900 census under any other names where she may have been living.