I'm a melanoma survivor too so can relate to your concern. I don't think bleeding necessarily indicates malignancy though. I've had a couple of bleeding ones removed which turned out to be benign. They do tend to bleed a lot & for a while.
I find if I tell a doc it's itching, changing, bleeding, they'll remove a mole pronto, due to my history of MM. If it concerns you, I wouldn't settle for 'it's fine' as I don't see how they can be so sure just by looking.
Hope you get to the dermatologist ok & get that one removed. Try not to worry & let us know how you get on.