I have very sensitive gums and they bleed easily since I am on 6MP. Almost daily I can strip off some skin of my gums and inside the cheeks. Yeah i know, gross. I use Sensodyne and am very careful with the flossing and only use soft toothbrushes and be careful of how much pressure I put on the brush. Strangely the mouthwashes that burn a lot do better work for me than the ones without alcohol.
I checked with my dentist and she also noticed that my gums bleed easily when I get my cleaning/checkup.
So for me, 6MP and gum sensitivity/gum bleeding goes hand in hand and my GI already "warned" me that this could happen when I was in the process of deciding if I should take it or not.
Just an idea.