The pair's first sexual contact - a kiss - took place on February 24 at the refuge where the victim was staying.
Ms Bex said the victim "flirted" with Peters and "made it clear to her that she found her attractive and therefore in her own words she encouraged it".
A couple of days later consensual sexual intercourse took place at the victim's grandfather's house when Peters was on duty, Ms Bex said.
Another sexual encounter happened at the same place on March 1, another in a hotel on March 8 and later the same month the pair had sexual intercourse in the "lavatories at McDonald's", Ms Bex added.
The relationship was revealed when the victim told a member of staff at the refuge that she had broken up with Peters.
The court heard that the victim said she realised that Peters was never going to leave her girlfriend.
"And to use her own words, she was tired of being her dirty little secret," Ms Bex said.
At Peters' request, the victim deleted the app on her phone that hosted messages between the pair. Peters threatened to kill herself, and the victim cut her wrists resulting in her having to go to hospital.
In an interview in November, the victim described having been "in love" with Peters.
Asked if she thought Peters was taking advantage of her, Ms Bex told the court the victim said "no" and said the victim added: "It was just two people who fell for each other in bad circumstances."
Judge Leonard said it "beggars belief" that Peters, someone he said seemed to be so admired, did what she did.
Referring to the victim as "V", he said: "It is clear that V loved you and you loved V and you are not being punished for that fact."
The judge said the police force was "shocked" by her actions, saying: "I accept that your behaviour was out of character."
But he added: "You must have realised as soon as it started how inappropriate your relationship was."
The judge told Peters her actions will bring her career to an end.
He pointed out that while the relationship was consensual he does not accept that her behaviour was not "predatory".
This article was originally published by the Daily Telegraph.