I mix my white pigmented “fast dry” wiping stain with a little bit of gray stain of the same brand. The ratio of white to gray depends on just what look you are trying to achieve. You can also mix these stains with a red mahogany color to achieve a pinkish wash to the floor, or even a universal tint of blue or green. The added dark pigment (don’t use too much) will make the stain easier to use, and the white wash color you were expecting will come though. If you wish to know the specific brand I use here in Toronto, Canada, e-mail me at joseph@woodfloordoctor.com and I will try to find someone that will ship it to you. Otherwise try the Bona Kemi brand wood stains or the Dura Seal pastel white, these are what most pros try to use anyway. These brands are available nationally, so these are what are practical for me to mention in a web article.
Another more tricky way to white stain a hardwood floor is to sponge the wood with distilled water, and let it dry overnight. You will then find all the pores of the wood open and willing to accept even the lightest colored white stain. I used this method a few times in the past, but it is risky in a humid climate. A blue-black fungus may show up in red or white oak overnight, if the wood has dried too slowly. These are visible as little black dots all over the floor, and can only be removed with a fine sanding, defeating the whole sponging exercise. You should try this only in the winter when you can really dry the floor with the heating system. And ventilate after you sponge, so the wood dries fast. I don’t use this method anymore, too risky.
You could also consider sanding the floor only to 60 or 80 grit. This will help the white stain pigments lodge in the wood better, but won’t be as smooth. This may be fine if you don’t mind seeing some sanding lines in a floor for a more rustic and textured finish.
Oh, and by the way, you must finish your white floor with a clear finish, else you will in time, have yellow toned floors. The clearest finishes on the market are the acid cured or Swedish finishes. Glitsa and Synteco are two of these. The problem with these is that they emit formaldehyde gas for up to 90 days after application. A bit safer are the catalyzed water based finishes. Bona Kemi and Basic Coatings are the major producers of these. The catalyst is very toxic to the skin and is a possible carcinogen, so handle this stuff carefully. And the last choice would be a clear lacquer nitrocellulose finish. But be sure to read all about this explosive finish in my Lacquer Floor Fires article in this site. The Swedish finishes are also about as flammable as the lacquer. Consider having a well-seasoned pro apply any of these flammable or poisonous clear coatings.