When Sweets was so, so unaware of what he was getting into with this anthropologist…
When Brennan sweetly revealed Booth is the only one to give her a nickname…
When she didn’t know what that meant, but she was trying…
When she interrupted her husband’s wedding vows to be adorable…and gorgeous!
Boots & Blazers 
Whether it was the way ED played the scene or maybe intentional on the part of the writers, sometimes when Brennan played with phrases (i.e., said them wrong), I thought she did it for the reaction she knew she’d get from Booth. Not that Brennan would ever ‘play stupid’ for a guy but it was almost as if she knew she’d get it wrong, she knew he’d correct her, and they would both enjoy the moment. Her smile in that fourth photo (Super Ball set) is the smile of a woman who thinks her guy is adorable, and matches Booth’s amusement in the 3rd photo.
It’s probably a bit of both. The writers probably gave her things they knew she would do amazingly, and then I think DB/ED come up with some of the cute stuff when they practice because they are perfect 🙂
And I could totally see Brennan “playing stupid” (for lack of a better term) as a sort of way of flirting. It’s not typical flirting, it’s intelligent word play flirting. I could totally buy her doing that.
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