Rey had been away from Finn's bedside for one of her breaks, comfortable letting Poe stay while she did so. If anything happened with Finn when she wasn't there, BB-8 would come get her immediately.
She had the strangest feeling, though, as she was walking back. She had a certainty that Finn had just woken up while she wasn't there. She couldn't have explained how she knew— or rather, she could only explain it by the Force, and that wasn't exactly something she knew enough about to explain just yet.
By the time BB-8 started wheeling to retrieve her, she was already at a run and BB-8 had to hastily adjust direction to follow her. She nearly screamed with happiness when she saw him looking up at Poe. "Finn!" She was all set to launch herself at him for an embrace, but since that much movement or contact with his back was likely against medical advice, she settled for wrapping her arms around his head instead.