The Doctor had flopped down into the seat next to her, finding no reason to act like a normal person considering he'd assumed it was someone he already knew very well. "Oh, I guess I'm used to it," he said with a shrug; why on Earth had she been sitting giggling at him anyway? Maybe she'd been amusing herself, waiting to see how long it took him to notice her... yes, that had to be it. "Suppose not, it didn't stop me finding you," he agreed, leaning forward to check out the title of the book before leaning back again, and giving her a frown. A reason to hide? "I shouldn't think so. I hope not!" he answered, laughing a little with confusion.
He raised an eyebrow as she said she'd been watching him... but as the conversation continued he started to realise... that either Rose had developed a strange kink for pretending they were strangers, or the woman... wasn't Rose after all. Without really thinking about what he was doing, the Doctor leaned close to the woman and inhaled. Ah - luckily his Time Lord senses only needed that much to confirm his suspicions.
"Huh. I'm sorry, you look a lot like a friend of mine," he commented, pulling back again. "Exactly like, actually. Slightly different hair, a bit more..." he scrunched up his nose, trailing off again. A bit more what? Any way he ended the sentence wasn't going to be good. "Sorry, I'm the Doctor," he explained, holding out a hand for her to shake.