One Good Earl Deserves a Lover by Sarah MacLean. Book 2 in the Rules of Scoundrels.
I have to say this was one of my favorite Jane sightings because it wasn't a woman admitting to reading novels, especially those by A Lady. In this scene Pippa and Cross are entering gaming hell where Cross is an owner, the door man is against letting Pippa in since she isn't a member.
Aariel returned to his book, ignoring them both. Pippa tilted to see the book in Asriel's hand. Her head snapped up, eyes meeting his in disbelief. "Pride and Prejudice?" (pg 177)
There is some more back and forth about her not being a member and she comes close to breaking a rule she doesn't know about (it's a rule we learn about in book 1). Asriel says some snippy things and Pippa, not one to be outdone returns fire with:
She tried, nonetheless, with a wide, friendly smile. "I do hope we shall meet again. Perhaps we could have a reading club of sorts. I've that one." She leaned in. "Have you reached the part where Mr. Darcy proposes?"I'm really enjoying this series. It's connected to a previous series by MacLean called Love by Numbers. If you enjoy regency romances and you haven't read these yet I highly recommend them!
Asriel narrowed his gaze on Cross. "She did that on purpose."
Pippa shook her head. "Oh, I did not ruin it. Elizabeth refuses." She paused. "I suppose I did ruin that apologies." (pg 178)