How come Mumei's pistols can kill Kabane? In episode 5 of Koutetsujou no Kabaneri, the jet bullets are presented — freshly developed based on Ikoma's explosive-steam hybrid gun. However, Mumei has her steam-powered pistols from the beginning and is also able to kill Kabane with one shot.

Since the blades on her pistol are reinforced with Kabane "fabric" I assume someone else had similar ideas regarding the improvement of anti-Kabane weapons, and that this is the reason why Mumei's pistols are that strong, though I'd say using explosives to improve the gun force is still quite unusual idea for a steam powered world. But even if we say Ikoma wasn't the first one with these ideas, why isn't anybody else using this technology?
As you know and heard of, Mumei is a kabeneri (half- human and half- kabane). And apparently, once you become a kabeneri, your abilities as a human increases vastly. For example, your speed and strength increases. Remember, when she talks with Ikuma inside the train, she says "if I remove the ribbon around my neck, I could use my real abilities". But she doesn't usually removes it, because as a side effect, she get's exhausted and sleepy. And also Mumei is seen in the anime as one skilled with martial arts. Therefore, due to her enhanced abilities- thx to kabane virus, it helps her to get Insta kill with her pistols. And also the ammunition which she uses are normal bullets and they are limited. 

I think this helped you in finding your answer and for more information about her, visit the link below.

http://koutetsujou-no-kabaneri.wikia.com/wiki/Mumei