Bonnie first met Jamie while looking for her mother (Abby Bennett). After Damon found out where Abby lived, Elena and Bonnie drove to her house. They rang the doorbell and Jamie found them and explained that Abby wasn't at home. After Bonnie told him she was Abby's daughter, he invited them in. In the episode, Do Not Go Gentle, Jamie is Bonnie's date to the 20's dance. At the same evening they made out but got interrupted by Damon, because he needed her help.
Jeremy Gilbert soon joins them which leads to a Bonnie-Jeremy-Jamie interaction.