Sorry you had trouble with the texture packing. There are many packing options that are useful in various situations.
Bleeding prevents artifacts that occur when filtering (the selection of pixels when scaled) mixes colors from adjacent pixels. So you have a green pixel (RGBA 0,1,0,1) next to a transparent pixel that your image editing program has made red (1,0,0,0). When the image is scaled, filtering can pick up the red color from the transparent red pixel and you'll end up some red mixed in to your green. Bleeding extrudes the colors from non-transparent pixels into transparent pixels so filtering doesn't introduce unwanted colors. It looks like this:
Here is a page with more pictures.
The problem described is only an issue when not using premultiplied alpha. When not using premultiplied alpha, blending is actually incorrect, even though it may often look close to correct. Premultiplied alpha is always preferred and this problem doesn't occur.
Bleeding is unlikely to cause black edges. More likely is that premultiplied alpha makes your images appear to have black edges when opened in an image viewer. This is actually correct and the black edges won't be visible when the images are rendered for premultiplied alpha in your game.
If your problem is that you can see edges of images when rendered at runtime, then you can fix this by using premultiplied alpha in the atlas and choosing the correct blending for premultiplied alpha at runtime (eg