If your dog is vomiting with blood, it needs to go to a veterinarian straight away to find the underlying cause.  For more information about causes of vomiting, you can read this article:

https://www.vetbabble.com/dogs/health-dogs/vomiting-dogs/

As mentioned in the article, if there is blood in the vomit, your dog needs immediate veterinary attention.

In the best-case scenario, it is a one-off event and after a full physical exam and history, your veterinarian will be comfortable discharging for monitoring for home.  However, you will need a thorough physical exam to help try and localize where the problem is and if further diagnostics are warranted as it could be something much more severe that needs immediate treatment.