Want white titanium? Think oxidation, e.g. Titanium Oxide (like you use for sunscreen). A layer of oxidized titanium should turn the surface white.

If you can figure out how to oxidize the inside of your cups, you'll have that white color you want.

I've seen some research papers on plasma oxidation of titanium that turned the surface a brilliant white color. Seems chemical treatment has potential to work at the right temperatures. But titanium IS valued for is ability to resist oxidation and not corrode.