Friend, I am sorry Bagel has been vomiting with specs of blood I am sure this must worry you. In response to your question, anytime we see blood in the vomit we need to assume that there could be something damaging the wall of the upper gastrointestinal tract, things like a foreign body, parasites, infections, ulcers, etc. less likely the patient can also vomit blood with a systemic disease like coagulation disorders, toxicity, etc. Unfortunately on history only it will not be possible to determine the exact underlying cause, I am sorry. Bagel would need to see your family veterinarian for a hands-on examination, x-rays and blood work as an initial screening test. Treatment will be based on exam and test results. In the meantime, this is what you can do:
1- Do not give things like Pepto Bismol or Imodium. Start her on Pepcid AC (famotidine) 10mg 1/2 tablet every 12 hours. You can buy Pepcid AC over the counter in any pharmacy.
2- No food or water for 4-6 hours. Need to give her gastrointestinal tract time to rest.
3- After 4-6 hours offer a small amount of water. Wait half hour, if no vomiting, offer a small amount of rice (50%) and boiled boneless chicken or ground beef (50%) 4-6 times a day. Keep on this diet for several days then wean into regular diet.
4- Follow up with your family veterinarian for a hands on examination. If cost is a concern I would look into your local ASPCA or Shelter where they often offer veterinary services at a lower cost.
My goal is to provide you with excellent service - I hope I've provided the information you were seeking, if you feel you have received anything less, please reply back as I am happy to address follow-up questions. Kindly rate me when you are done.