Why do you assume he doesn't know her? If you read the chapter there is no way to know if he knew who she was or not. I always figured he knew the woman, and that was why she threw the kiddo at him...because she knew he was a safe person to ensure his safety to. Seriously think about it. If you know a group of crazies are trying to murder you, would you throw you kiddo, and demand safety for him, to a guy swimming in a river, wearing a suit? I wouldn't!
So the King cheated on the queen and his misstress was Biebke. Biebke is Ryuu's mother. Daniel is a hitman who was supposed to kill the King but his accomplice(Simon) did it in his stead in a more fashionable way. Ryuu is going to be saved and thrown by a woman off a bridge. But it doesn't make sense? NO?
Bcs, in chap 1, when Ryuu is thrown off Daniel should've recognised the woman's face because if she's not a high graded person she's at least a servant that he must have encountered. Also, wouldn't he have recognised Ryuu's face?
http://www.mangago.me/read-manga/papa_s_assasin_ryuunosuke_wa_tonde_yuku/mf/v01/c001/13/