Bill put her arm around the Doctor's waist to steady herself as much as to just have something solid - and he was solid. "I wouldn't want to be anywhere else," she told him, though she sort of understood him in that moment. He knew something - something dire, something that made him afraid for her. But she didn't want to know.
She limped along to the chair and settled in, holding tight to the edge so she didn't just slide off with the movement of the TARDIS. "I expect John might want to come check on me at some point," knowing that more than guessing. She'd been talking to him and Sherlock a fair bit after all. Plus he was a proper medical doctor and she'd just been whisked away by a madman in a box.