Bill smiled, though it wasn't the laugh that would have left him at that just a few weeks ago. Just a smile. He did brighten up a bit at the sight of the broom however, because there was nothing that took your mind off things as well as a broom.
Taking out his wand, he summoned his own, then nodded at Remus. "I believe you do," he said. "And I think I could manage to answer a few questions." In fact as long as those questions weren't how are you? or any version thereof. Flying, helping out with research and putting spells on Hogwarts, those were all easy things to do. Things that distracted him from the empty house and the empty bed and the whole that was his heart these days.