When a mole bleeds, scabs, and changes shape, the cause 99%+ of the time is irriatation or trauma, most often from picking and scratching. If the mole continues to trouble you (and it must, or you wouldn't have asked 6 doctors about it), then I think you should see a dermatologist or plastic surgeon and just get it off. Even if isnurance doesn't cover it, this wouldn't be expensive (and sicnce the mole has bled and changed, perhaps insurance would cover it.)
Anyhow, I would suggest you just leave the mole alone and apply an antibiotic ointment like bacitracin daily for a week or so, then show it to a doctor for diagnosis and consideration fo removal.
Best.
Dr. Rockoff