Any tricks to make this background true white?

I think the easiest way would be to use an adjustment layer of your choice, like Selective Color or Curves (or even both, just copy the mask later on). Make the background look other way you want, don't mind the bullets.

When happy with the background, make a mask on the adjustment layer(probably you already have, I think that is photoshop default). Grab a soft brush, use black, and paint in the mask over the highlighted areas on the bullets.

It shouldn't take longer than a few minutes. I know some people are afraid of brushes and masks, but they are just perfect tools for something like this. And very quick too.