I wouldn't like to hazard a guess as to whether this is diabetes related since I don't really know how long I have had diabetes (diagnosed in Dec 2004) or how long I was in a pre-diabetic state.
But what I can tell you is that ever since adolescence, I have suffered bouts of nosebleeds - just as you describe. Sometimes they last a week or two, sometimes shorter. Sometimes there is a gap of years between bouts, sometimes months. I haven't tied them down to anythng. The only thing that my Dr can say is that I must have a weak vein and if it ever caused a serious problem (i.e. the bleed doesn't stop) then the answer is for it to be cauterised.
I stop my bleeds in a couple of minutes by stuffing tissue up my nostril.