Is there such thing as white wheat berries?
Sorry, my answer was incorrect (it used to say that there is no white wheat). The only defense I have is that such newfangled things like white wheat have not yet reached my part of the world (is Europe really that old-fashioned?). Big thank you to Jefromi for correcting me and teaching me something new. 

"Normal" white flour is, as I described in the old answer, made from the inner part of the wheat berry, discarding the yellow-brownish hull. You can't make this at home. But it turns out that there is such a thing as white wheat. When it is used to produce whole flour, the result is a flour which is white in color (but behaves more like whole flour when baked, and has nutritional properties like whole flour). So if your definition for white bread is just based on color, it is probably possible to make white flour from white wheat. They say that the taste is milder than "yellow" whole flour, too, closer to the refined white flour. But from what I read, you probably won't be able to produce a fluffy soft baguette with it, just because it bakes differently. 

If you want to make flour which is equivalent to the common white flour in the supermarket, you are still out of luck. The machines for removing the bran are too complicated, you can't do it in a grinder (look here for a patent for a bran removing device). But if "white whole wheat flour" is good enough for your purposes, I don't see a reason why you can't grind albino wheat at home.