That seems like a perfectly reasonable request when she doesn't know him that well and he has that aura of creepiness, and for all he knows vampires are really paranoid anyway, and all he wants is for her to be safe and comfortable anyway, so he nods. "The guest room does have a lock on it. Both bedrooms do, really, but I don't use that one much." He does in fact keep his personal bedroom locked, since... it's not really a "bedroom" per se. "I can give you the key, so you won't think I might use it or anyone else could get it."
no subject