Calling someone eccentric the way she is implies a whole lot despite Shaw's brief description, and she's used to reading between the lines when it comes to Shaw. Respect Michonne, see how far she can get teasing the Doctor.

"Can't wait to meet him." She's genuinely excited with a description like that. "We almost there? I think I'll need some help warming up."

Root can't resist the obvious invitation, though she isn't expecting anything to come of it necessarily. She's just never going to stop trying when Shaw keeps signaling she's receptive to it. And if they're going to have a second chance like this, she'd be a fool not to take advantage of it to the maximum extent possible.