Silentkit would never bully anyone (she's the target type) but she's very small, quiet, and doesn't appreciate noise. Maybe Charcoalkit could bug her until Silentkit snaps (in her own way) and tells her to leave her alone?
Silentkit doesn't break rules often but she hates being told what to do and is learning to stand up for herself and be more assertive. Charcoal could make a lot of noise around her and could send Silent into a meltdown, which would make her dislike her.
Maybe after a while (like when they're apprentices) they could warm up to each other, but it's up to you.
Also I know it's not what you're looking for but Scorchstrike could mentor her if you need it, they have a theme name! @
Shadeleaf