A judge at Basildon Crown Court was told that a psychiatric report on Denise Giddings, from Basildon in Essex, said she had been "extremely disturbed psychologically" when she took Karli Hawthorne from Basildon Hospital last December.
Judge Philip Clegg adjourned the case until 17 April, for probation reports to be prepared. After the hearing Detective Superintendent David Bright said that Giddings's guilty plea had eased the pressure on both her own family and Karli's parents.
Giddings looked close to tears as she heard the judge grant her bail, but warned that it was no guarantee that he would not enforce a custodial sentence.
After the hearing, Det Supt Bright said: "The guilty plea made by Mrs Giddings today reflects on the first-class investigation in which police received excellent support from the public and not least of all the media. We would not have been able to catch Mrs Giddings so quickly without the assistance of the media.
"And the speed with which Mrs Giddings was arrested brought about the safe return of Karli - because my fear, my very real fear, was for the safety of that young child.
"But with all those facts aside, today takes some of the pressure off Karli's parents and family members and also the Giddingses, to enable all parties to get their lives back together."
Karli was snatched from her hospital bed on 5 December. Her parents Tanya and Karl had to endure a 14-hour wait as police mounted a nation- wide search for the 6lb 15oz infant.
Their nightmare ended when one of Giddings's neighbours called police to say she suspected the mother-of-three.
On 6 December, police raided her Basildon home and found Karli safe and well sleeping in an upstairs room.
Yesterday Barry Spanjar,one of Giddings's defence team, said she still denied knowing the reasons for the abduction. Claims that she carried out the abduction in an attempt for a reconciliation with her estranged husband, Leslie, were false.
Mr Spanjar also denied that Giddings, whose children were all boys, had grabbed Karli because she was desperate for a baby girl.
"It could just as easily have been a boy ... She took the nearest baby. That baby could have been anyone's," he said.