I'm not sure which white spot you're talking about here now. But I'll briefly explain what happens.
Okay so Betta's in stores, and this goes for all fish in stores, are super stressed out all the time. They aren't meant to be in such a close environment with other fish like they are and so they get stressed out very easily. Also with not many water changes, that can stress them out as well. It's kind of like if you didn't change your underwear for a week and didn't shower either, yeah it's kind of gross.
So from all that stress, they tend to loss their colors and become pale. More often than not you'll see what we call Stress Stripes which are generally two black horizontal lines running down their body. They can pale so much that you see those stripes and the in an instant go back to their normal color. So what you see in the store is not their true colors, that's them being stressed. So now that she's home and more content, she's starting to show her true colors.
Many fish have iridescence on them which is the blue that you see on her. It's what makes them look shiny, that will also "disappear" when they get stressed out, or seem to disappear at least. And then when they are content and no longer afraid again, it will come back.
I believe the white that you are referring to is right behind her gill cover, that is just part of her pectoral fins. It's a joint that they all have and you see it more when she's fully colored up. If that's not it just let me know