I think it feels a bit too fast in the anime because most of the time they've spent together has been off screen. If you interpret it as "Asuna has been gunning at him for a while now and this latest attempt to party together was merely the most recent move" then it makes more sense. Kirito also seemed to quite casually grab her hand when they met at the beginning of this arc, so we just have to assume they got close off screen.
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