"What? No, it's fine — if I could get a room to myself, I would already have one." ... wait, that sounds horribly rude. "My title doesn't actually carry much weight here, possibly because there's quite a lot of other royals from other realities. In this realm, the privileges of nobility have to be earned..."

And she hasn't quite finished that quest line yet, so to say. But she decides not to bring it up, instead pointing out...

"I'm not sure if that would matter, at any rate. There's not enough rooms for everyone, and reserving some would just make the problem worse for everyone else." She gives an awkwardly polite smile. "So... please, don't offer to give up your bed on my account. It's fine, really!"