Williams, who was in a same sex marriage at the time, hugged the girl and asked her to stroke her hair before she began fondling the teenager and saying she loved her. She has now split up with her partner.
Police were called after the girl's mother checked her daughter's mobile phone to discover the pair had been sending each other a large number of intimate text messages.
Williams, from Thornton-Cleveleys, Lancashire, later claimed the teenager had made sexual advances towards her - but confessed: "I didn't handle the situation very well."
At Preston Crown Court Williams admitted sexual activity with a child and was jailed for 32 months.
Judge Christopher Cornwall told her: ''This was not a moment of madness, you allowed this to develop into a continuing relationship, arguably doing more damage to this girl in the process and you were nearly three times her age.
"Boys and girls of that age don't necessarily understand what they are becoming involved in - and they don't understand the consequences. My impression is that this young girl didn't have control over what was happening. "Her account to the police portrays you in a grim light - taking advantage of a 15-year-old.