What color grout are you planning for the floor? I hope not white if you are worried about it getting dirty. I'd go with the white tiles and a pale grey grout, then use a grout sealer. That should be good for the future.

There are sources like hextile.com that sell the flat historic hex tiles in white and black, and also American Restoration tile.

FWIW I installed 3 inch cararra hex tiles in my bathroom about 8 months ago with pale grey (Silverado) grout. They were sealed, of course. So far no problems, and I really like them.

Try checking over on the bathroom forum. Use the search tool. There have been a number of discussions along the lines of your concerns.