Sorry, no. If Babbitt really was shot in the neck, there could easily have been plenty of blood sprayed from damaged carotid arteries. Some say that she was shot in the chest, which could also have produced plenty of blood. In that very crowded space behind the doors, her blood might easily have been smeared onto many people. No fake blood would have been necessary to attract the interest of reporters.
This bothers me: I tried to track down details of Babbitt's funeral, and failed.
How about filing a freedom of information request for her death certificate and autopsy.