No, it is not normal for a female dog who is guaranteed to be pregnant to be bleeding. Bleeding in a pregnant dog can be a sign of a miscarriage, and therefore a veterinary exam would be needed for the investigation. In some cases, the bleeding may stem from other causes such as trauma or maybe the blood is coming from the urinary tract, as it is common with urinary tract infections. Bleeding disorders may also be a cause, as it happens with exposure to rat poison.
In an intact (not spayed) female dog who is NOT pregnant, bleeding can be worrisome, considering that this may be a sign of Pyometra. Pyometra is a uterine infection which often starts within 3-4 weeks following the heat cycle.