They can bunk up! The opportunity for "turn your back while I change" amuses me, but it might also be a good opportunity for her to see that Davos wasn't lying about the "knife in the heart" thing.

I can see him potentially getting at least slightly rough during training simply to warn her not to be overconfident. He'd also probably continue to try to steer her to spears and arrows, but hey, Jon, not everybody gets a spear or a pike and not every battle has bows and arrows.