Pavelka and the singer and actress were reportedly flirty and affectionate while on their quiet date.
"They had lunch and held hands across the table," the source added. "They started to kind of nuzzle and Jake seemed so into Kristin. He looked like he was starstruck and in love at the same time -- just beaming and smiling the whole time."
The 34-year-old pilot from Los Angeles, CA -- who starred in The Bachelor's fourteenth season in 2010 after originally appearing on The Bachelorette's fifth season -- reportedly dated Ashley Ann Vickers, a model who competed on the second season of CMT's The Bachelor-like Sweet Home Alabama reality dating series, in late 2011.
Pavelka and Girardi both awkwardly competed against one another on Bachelor Pad 2, which aired in the Summer 2011, but Girardi made it much further in the game as Pavelka was eliminated during the season's third episode.
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