Hmm, I don't know much about bettas, but in school I loved genetics.
From what I remember white is a very tricky color, it's not a dominant.
The dominant colors in bettas are red and blue. I can't tell you which color would produce the whitest fish, but much of the fry's color will not only depend on the color of the parent, but also the parents of the parents, since some genes can lay dormant within the fish and only show up in the next generation.
Some info I found.
On yellow bettasInfoinfo 228 articlesIf these sites don't answer your questions you can always try looking into guppy genetics, I know those fish are being in many genetic studies.
Some color genes may be gender related, that's the reason only female cats are tabby and most red cats are male. I don't know if this counts for bettas though.
Good luck!