You aren't likely to have a lot of luck finding a white yarn that felts well. If it's pure white, if it's been bleached, it won't felt, because the bleaching destroys the qualities of wool that make it felt. Even natural white wool (which is rarely pure white, but more of a creamy off-white) doesn't felt very well.
"Choose your friends by their character and your socks by their color. Choosing your socks by their character makes no sense, and choosing your friends by their color is unthinkable." http://RoseByAny.BlogSpot.Com
The only one that I've found that felts at all is Cascade 220 - I've also had luck with Paton's Classic Merino. Still I'd do a swatch to felt before you do a project just to be sure. Sometimes the wools they use change and thus changing the felting properties.
Brown sheep white will NOT felt well and a lot of people have had problems with some of their lighter colors too - like yellow and pale pink.
I was able to felt a red white and blue purse with Knitpicks WOA. Just be aware that the blue ran a little. I now understand that putting vinegar in the water will help with that. I used the dye your own "color" for white.
Manos and Handpainted Yarns/Malabrigo off white yarns also felt very nicely. I've had wonderful success with even Kool Aid dyeing the off white Cascade 220 and felting with it. Regardless of color, I always recommend that you felt a swatch before knitting your entire project.