Long post, and I hope you can bear with my Engrish, but here’s some speculations on why Ririha is “bullying” Yuzumori based on what we know so far.
We can all agree that Yuzumori doesn’t get along with her classmates because she doesn’t find interesting enough what they do or talk about. But, as a kid her age, Ririha probably believes that somebody who doesn’t spend time with their classmates must find boring, therefore, looking down upon what they like and what they do (and looking down means that you put yourself above the others).
When Ririha is first introduced she’s commenting boys with her friends. The impression I got is that of a young leader. Of course, they could be just good friends, but leaders need approval and acceptance, and having somebody in your classroom of the likes of Yuzumori who “maybe” used to be your friend (but I doubt this being the case since, if you’re friend to somebody, you’d know if they have siblings) as much as having somebody who’s never shown any interest into you can be challenging, not only getting on your nerves because they don’t see you fascinating enough to befriend you, but because it implies a negative opinion on your persona. Basically, Yuzumori can’t be bother by Ririha, but Ririha is upset by Yuzumori’s lack of interest in her.
When Ririha and the other girls cross path with Yuzumori, she’s the only one concerned with Yuzumori’s presence. I suppose it hurts her, it offends her that Yuzumori so blatantly ignores her while the other girls don’t seem to mind it (one of them actually has to think about who’s this Kaede Ririha’s mentioning). Then, Ririha chances upon Mimika and Yuzumori and she witnesses Yuzumori’s cute and warm smile. She is stroked by that: she’s not glaring, there are many emotions in her stare (and when it comes to it, Ejima Eri makes most of them tricky ones to crack), but definitely there’s not just anger in her eye.
My point: Ririha has romantic interests toward Yuzumori. I suppose seeing Yuzumori smiling moved something in her: she understands that “stoic Kaede”, the girl she calls by her first name - which suggests a level of intimacy that, despite she keeps it for herself, Ririha definitely feels - that same girl she likes has somebody whom she deems appealing enough to be wanting to spend time with them, somebody who makes her SMILE. (and, doesn't it irritate you when the girl you like is happy because of someone else?)
I doubt we’ll get much drama out of this, but I’d like it if she’ll help to push Yuzumori/Mimika relationship to a different level. Maybe Mimika will have to prove that she does love only Yuzumori. Maybe it’ll clear Yuzumori’s mind on what exactly she feels for Mimika (although we get a glimpse of that every time Mimika makes cute faces and Yuzumori's eyes shine and her heartbeat accelerate).
Also, there’s that one detail that never cease to amuse me when somebody glances at their love interest in a manga, sakura petals. We got them when Mimika spots Yuzumori the first time, we got them now when Mimika says “let’s play lots and lots” and Yuzumori’s looking at her, and we got them when Ririha watches Yuzumori walking away at loss of words.
On a side note: I don’t agree with Ririha being a yandere, not even with her bullying Yuzumori (I need more than a kid "threatening" another kid to say they’re bullying them). She comes at Yuzumori alone and she’s probably too scared of her own feelings that the ending result is more aggressive than she intended to. (She might just want to rob Yuzumori’s first kiss.)
