While I'm glad the kid is ok, Baek Han is kind of breaking bodyguard 101 here. I know the author is trying to emphasize what a nice guy he is but the whole point of a bodyguard is for them to remain at their master's side at all times so they can protect them in the case of a sudden event or attack. Here he leaves her, among a crowded area near a rushing flooded river, to go chase after a commoner. Moreover, he simply told her to wait there and rushed off. As a servant of the Empress, he should have to wait for her command before doing anything outside his guard duty. At the very least, he would normally be expected to get permission to leave the Empress' side, and truth be told, even then he really shouldn't as her guard leave since there are no other guards present to cover for his absence.