Hi, I love that dress! As others have said, I definitely recommend looking into a minimizer bra of some kind. If this won't work, there might be some other things you can try. They make so many different types of camis now in so many colors, you may find something that complements the dress. If that's not in the cards, how about taking your dress to an experienced tailor? They may be able to make a slight alteration to keep the bust area from opening up too much, or even sew in a small, matching swatch that keeps the V-neck from appearing too low (I had to do that with my wedding dress).
Anyway, much luck to you! I hope you find a way to rock that dress because it is gorgeous! Keep up the good work and don't let this discourage you.