I know this is 4 days after your question, and probably now you have resolved it. I know how you feel about going out the door for yet another doctor appt., but your nurse would probably tell you if she thought it was something to worry about. I had quite a lot of bleeding from the stoma too, but it didn't really drip, just collected on and around the stoma. It would continue while it was being cleaned. Sometimes mine would bleed into the bag lightly. It is scary, but I seemed to survive and, yes, the nurse assured me it was normal. Especially as we cleaned it during changing as well as around the edge of the barrier ring between changings. Often the top edge of the barrier ring was bloody from continual irritation. We used very soft cotton cloths, but it still bled. Also, mine never totally healed even up to the point of my reversal surgery. It would always be "picky" and felt like the bag was pulling on the top of the stoma. I never named mine, but thought it resembled the creature coming out of the guys chest from the movie "Alien". We all got a good laugh out of that, but then again, I guess my sense of humor may bit a bit on the demented side! Forgive me if I insult anyone. I also get "vegal response" sometimes when seeing blood from my body, so I can relate to freaking out over stome bleeding. Good luck.
Sue