If you want a great (but a tear jerker and not yuri) manga about the problem of bullying in Japan, I highly recommend the hugely acclaimed and widely discussed oneshot Koe No Katachi. http://www.mangapark.com/manga/koe-no-katachi
A really nice read, a deserving winner of the 80th Weekly Shounen Magazine Newbie Best Mangaka Award, and if this is a accurate portrayal of bullying in japanese schools, than it's definitely a serious problem.