If everyone adopted bitcoin, the velocity of the dollar would approach zero. Which means that inflation would go down, not up.
And yes, I would rather have my [savings] account in a hard, non-inflationary currency. On the other hand, I can only earn interest when someone is willing to take a loan in the currency and pay interest on it. And I am not about to take out a loan in a hard currency when perfectly good inflationary currencies are easily at hand. So, you're going to have a hard time finding a bank that pays interest on bitcoins. This is why "bad money drives out good", aka Gresham's law.