Professional ballroom dancers usually don't go to college, at least not to study dancing. Many following the competitor first/teacher second route are well on their way and are already teaching lessons when they are in junior high school.
Some do manage to go to college and study something unrelated to dancing, a few even get advanced degrees, but the school is not training them as dancers. Some schools have ballroom dance teams, but again this does not provide professional level training. There is only one professional ballroom college program in the country, at Brigham Young University in Utah. It's an option, but keep in mind the fact that it's a church run school run by a church with much to say about daily life - good for those who agree, not good for those who don't.