How is natural monthly bleeding disturbing and disgusting in the context of "feral" Meiling? She's probably completely unphased by the occurrence.
I've never encountered a girl who bled enough to coat her hand in enough to drip off in huge blobs. Not to say it isn't out there, but I'd rather not run into it, personally.
Honestly, it strikes me more that Sakuya was preparing some "red tea", and it turned Meiling on enough that she let go into "Feral Instincts" (although I think the fanon junk about Meiling actually being a dragon is completely overblown) and got naked, and clung to Sakuya so tightly she clawed Sakuya in the inner thigh. (Explaining the inner-thigh bleeding.) Probably, this caused Sakuya to stab the victim inexpertly in the pain, since I doubt Sakuya would be so imprecise as to have gobs of blood on her hands while bleeding a victim otherwise.