PVA will shrink as it dries, so you could end up with a big basin in the surface, or it might pull away from the sides if you do it in one pour. Doing it in multiple pours/layers would work, but you'd have to wait for each layer to fully dry between pours to get a proper flat surface.
In any case, actually coloring it intrinsically would be a waste of paint. All you need to do is color the surface since, again, in scale blood that's any thicker than a coat of paint shouldn't be visibly transparent or translucent at all.
Fill it with whatever comfort prefers, and don't worry about color or bubbles or anything else but level surface and edges. Then float a layer of blood-colored paint over the top, and blend darker and flatter shades around the edges.