PC Andrew Hurst, 31, met the woman, who was in her 20s, in November 2014, during a cell watch after she had been arrested for shoplifting.
PC Hurst offered her assistance in getting mental health support from various agencies, however he continued to communicate with her via phone and social media.
The communication progressed to being of a sexual nature.
The woman’s partner became aware and notified Bedfordshire Police on March 30 last year.
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PC Hurst was arrested the following day and was suspended, he was jailed at St Albans Crown Court on Wednesday (November 2).
He had pleaded guilty at an earlier hearing to misconduct in a public office.
Assistant chief constable Mike Colbourne, said: “Protecting vulnerable people is a priority for Bedfordshire Police and we will not tolerate anyone who seeks to exploit those who are at risk of harm.
“We expect the highest standards from our officers so It is incredibly disappointing that, despite the considerable amount of work being done across the force to raise awareness of vulnerability, that PC Hurst became involved in such an inappropriate relationship.
“We acted swiftly to suspend him as soon as we became aware of his deplorable conduct.
“Today’s sentence reflects how seriously such behaviour is viewed by the courts.”