"By the way, what's your name?" The man finally managed to ask. She'd been expecting him to for ages, but apparently proper manners were not a universal concept.
"Hermione Granger," she responded primly, extending a hand to be shaken.
"No it's not," he exclaimed with a look of indignant confusion. Her outstretched hand was ignored.
"I assure you, Doctor," replied Hermione, "I know my own name."
"But—" the Doctor began to pace, his trainer-clad feet squeaking loudly on the linoleum floor. He was scratching at the back of his neck again; it seemed to be a nervous habit of his, she'd observed in the few hours they'd been working (if by "working," you meant "fleeing from various ill-willed foes and slapping together plans of action at a moment's notice") together. This time, however, he was apparently incapable of forming a complete sentence, instead peppering the air with little incoherent bits of speech. "That's not— I can't have— that would mean— and, quite honestly, that's just— how did— impossible!"
"What's impossible?" Hermione asked, causing him to promptly stop pacing and face her. She was a little taken aback, not expecting him to react quite so suddenly.
"You're a witch," he stated, entirely too matter-of-factly for her liking.
"I don't know what you're talking about," she stammered, doing her best to look perplexed at his declaration.
"Yes you do," he pressed. "You've got magic. No sense covering it up."
Her defense crumpled inside her; she'd never been good at lying, had she? "How'd you find out?" She asked.
"That doesn't matter," the Doctor said quickly. "The thing is, that's impossible. Magic doesn't… can't exist."
"Yes, well," she sighed, "I thought the same thing about aliens, but you've pretty effectively disproved that stance, haven't you?" As if to prove her point, the young witch reached into her pocket to pull out her wand. Eagerly, he took it, turning it end over end and examining it in every way possible (including licking it… Hermione made a mental note to thoroughly wash and polish it as soon as she got home).
"How does it work?" He asked.
"Magic," she drawled, giving him a look. The Doctor laughed, realizing his mistake.
"Hermione Granger, I like you," he remarked with a wide grin. He handed the wand back to her, and then looked her up and down in a pensive (and decidedly unnerving) way. Nodding to himself as if making his mind up over something, he spun around and started down the hallway. Unsure of what was quite happening, Hermione realized, lost as she was, she had no choice but to follow him; she sprinted after him, falling into pace with his hurried footsteps. Then, just as quickly as he'd started, the Doctor stopped in front of a storage cupboard.
Opening the door with a flourish, he revealed what looked at bit like an old toolshed, apart from the fact that it said "POLICE" across the top, and was painted bright blue. He strode up to it and opened the door with practiced ease, running one hand along the wood in an almost loving sort of way.
"Come on, Hermione Granger," he smiled, gesturing for her to follow him inside, "time to see something really magical."