He does not have a spare bed. But that's a problem Strange can deal with in the morning! Right now, he's taking Shura to his bed and he'll just fall asleep on a chair or something.

"Step down," Strange briefly instructs Shura, as there's a small step going from the main room to the hallway. But back to making fun of her. "And yes, you're acting bashful. It's a loud, shouty sort of bashful, but bashful nonetheless."

As for the dragons, Aconite does get ground. Alistair's method of wrestling seems to be mimicing her movements until he finds something that works best. The gentle pushing and shoving continues.