You do not give bullets that will use standard alpha drawing a black background. Danmakufu counts #000000 pixels as transparency, and will not draw them. However, the black will mix with any degree of other non-opaque pixels of a bullet, and will taint the color. With alpha drawing, Danmakufu does not count this black as transparency, so your bullet ends up looking dark and shitty. This is why you keep alpha-drawn graphics with no background.
You do give bullets that will use add drawing a black background. Add drawing means that the color of each pixel will be added to whatever is underneath it. Black plus anything = Anything, White plus anything = White, and each degree of black and white is not added and added just the same. Because of this, there is no need for transparency, since an image with a black background will be drawn as if black was transparency. So, transparency is also counted as white pixels, thereby adding tons of white everywhere. This is why you give add-drawn graphics a black background.
To note, if you make a black background and overlay an add-drawn graphic on it, it will come out as it would if it were alpha-drawn.