well, since it's part of the White bundle, I'm not sure if they can just replace the white controller or if they have to replace the whole thing ( PS4, D24, Destiny ).
Have you opened up your copy of Destiny yet? if you haven't that's good.
Also, do they even sell the white DS4 by itself? if they do, you may be able to just get the controller replaced ( hopefully ).
generally, if an item is defective, and it is within the return period ( I believe it is 15 days at Best Buy ) you as the customer have the right to return and replace a defective item.
I would definitely call your store and talk to customer service. explain to them the situation and ask if you need to return and replace the whole bundle or just the controller.
if they don't sell the white DS4 by itself, you may have to settle for a black ( or different color ) controller.
btw......did you see my Xbox thread post yet? (hint: I won't be an X1 owner for too much longer.

)
edit: It looks like they do sell the white DS4 by itself. So, I would definitely ask them if you can replace your defective controller for a new white DS4.