I want to say Lirael by Garth Nix... although it's the second book in the series. Long, long time ago I read it, but I thought she was mentored by Sabriel (also the name of book one) who is an adult woman. (I could be wrong though!)
There's Queen Victoria: Demon Hunter by A.E. Moorat. Queen Victoria is mentored in martial arts and zombie killing by a woman called... Mrs Brown? Or Smith? My memory sucks today.