It could be an extra listed ingredient and in addition, the flour is usually brominated as part of the bleaching process. If I buy flour, I always buy "unbrominated". Yes, baking your own bread will solve the problem. That is what I am doing. I also avoid corn syrup as much as possible and most breads contain corn syrup, that is another reason why I bake my own bread.
Before you run out and buy a bread maker, please know that the baking tin is usually coated with teflon.