Different light-colored battings have different levels of transparency. Some white/natural battings will let a lot more of the dark backing to show through on the top. A black batting will dull down the white top a *lot*. If you really want white, I think Quilter's Dream white cotton batting in a medium or heavy weight will not allow shadowing. Warm and Natural will not allow shadowing either, but its natural color will change the color of white fabrics slightly. In other words, the batting can make white fabrics even whiter, or add a yellow/muslin tone to the whites.
If you are concerned about bearding on the back, using a black batting would help. However, then you need to be ultra-careful on which white batting you choose to use. I haven't tested, but I suspect that Hobbs 80/20 batting (one of my favorites) on top of a black batting would allow too much dulling of the whites on top. A bleached cotton batting that has been needle-punched is much denser and would probably work better to keep any of the black batting from shadowing through the white fabrics in the top. That's why, if you are going to layer, I would probably test out the QD cotton on top of the black batting.
The only way you are going to know for sure is to actually test the battings out on your top and backing. If you have any batting pieces on hand, try putting them between your top and backing to observe the effect on the whites in your top.