exporting sprite sheets that contain bitmaps leads to low quality sprites??

Hello,
I have recently created a graphic that contains a 2 bitmap images (a bow and an arrow). The problem is that when I go and export this graphic as a sprite sheet, there is a very ugly grey edge that appears on each sprite which is seen in the attached image. Removing the bitmap objects from the graphic makes the ugly edges go away but that defeats the purpose of the animation if I get rid of them.
I have tried tracing the bitmap images, the bow turns out fine but the arrow looks weird so I was wondering what else I could try to fix this
What seems to be the only solution at this point is to create a seperate graphic for each layer and then overlay them.