You are right to focus on the importance of blood in this excellent short story. Let us remember that blood is a crucial element of catching this virulent disease, and marks the beginning of the end, as the first paragraph of this tale reminds us:
The "Red Death" had long devastated the country. No pestilence had ever been so fatal, or so hideous. Blood was its Avatar and its seal--the redness and horror of blood. There were sharp pains, and sudden dizziness, and then profuse bleeding at the pores, with dissolution. The scarlet stains upon the body and especially upon the face of the victim were the pest ban which shut him out from the aid and from the sympathy of his fellow men.
Note the way in which blood is so closely related to the Read Death, being its "Avatar and its seal." Blood is something that marks the presence of this highly contagious disease, and also something that is a clear indicator that the end is nigh. Blood is therefore symbolic of both death, but also the panic and fear that such an awareness of the closeness of death creates.
Blood symbolizes death or, more precisely, mortality. The "redness and horror" of blood is the "avatar" of the disease--which leads to sudden bleeding from the pores and a quick death. Much of the story has to do with the juxtaposition of the revelers with the passage of time (represented by the chiming clock) and the approach, with passing time, of mortality, represented in the story by the masked figure. While the prince thinks he can avoid death by locking himself and his friends away from the outside world, what the story shows is that time and mortality are ever present. In the same way, the blood, which gives life as long as it is "hidden" inside our bodies, becomes the sign of death when it is "unmasked" and becomes visible (through bleeding). For all of Poe's emphasis on imagery in the story, the colors of the different rooms and so forth, there is a sense that ultimately the "artifice" of the prince (as "author" of the ball) or of Poe himself (the author of the story) will lead to blood and death.