Mr Gibson, 28, was shot in the stomach and thigh in an alley near Divis Tower on 24 October. He died in hospital.
Margaret Goodman, 56, from Ballymurphy Parade, was arrested in Belfast on Monday.
She has also been charged with possession of firearms and ammunition under suspicious circumstances.
Detectives say new DNA evidence has come to light which connects Mrs Goodman with the alleged offences.
Mrs Goodman's bail application was opposed by police due to concerns that she would "leave the jurisdiction".
However, a judge ruled that the risks were not sufficient for the accused to be detained in custody and granted bail.
Mrs Goodman's husband, 58 year-old Malachy Goodman, has previously been charged with Edward Gibson's murder and is awaiting trial.
A 68-year-old man and a 70-year-old woman also face charges of assisting an offender and failing to provide information.
A woman has appeared in court charged with the murder of Edward Gibson in west Belfast in 2014.