Maybe she was on an errand from her guardian or something I don't know. But probably had to go so those two can be alone considering she broke character and was embarrassed she probably couldn't do it with her. So the mangaka decided that she ran an errand so they can be alone. (Just a guess)
@maverun
As an Korean-American who follows Japanese culture it is indeed very rude to say a name without suffixes when meeting with anyone. The only time it is ok is when you are very intimate or close. On the contrary if two people have the same family name it is okay to call them by the first...