First things first: some schools have specific rules about what to do if a student wants to date a professor -- and vice versa. So if that's the case at your institution, know that the answer to your dating question lies in the faculty handbook instead of on this website.
If you're at an institution where there aren't specific rules about dating, there are most likely some guidelines. Dating between professors and students is often not looked kindly upon. Professor/student relationships -- even when a student is an older student -- has an unequal power balance to it by nature. Even if the professor isn't the student's professor, there's a chance he or she can be. And that professor holds power over the student in all kinds of ways, from influence with the professor's colleagues to being a member of the campus faculty in general. Many schools look down on professor/student dating because of these reasons. What's to say a person who isn't your professor now won't be in another year or two?
Additionally, other students may perceive you as having an unfair disadvantage because they are not having a relationship with a professor, too. Say you're dating a professor and, during your conversations, you hear about some changes coming down the pipeline in regard to core requirements. Or you get to go to fancy campus events that other students aren't usually allowed to. Or your professor boyfriend/girlfriend helps you figure out which classes to take and get you the classes you need. In your mind, you might just be enjoying the benefits of a nice relationship. But in other students' minds, you might be enjoying something they are unable to get unless they make the same choices you did.
Lastly, dating a professor can have difficult consequences over the long-term. Say the relationship doesn't work out. What will things be like for you on campus? What if your ex-boyfriend/girlfriend/professor isn't as nice as you thought and wants to create trouble for you? What will the climate on campus be like for either of you if you have a bad break-up?
If you're absolutely convinced that your professor is the love of your life, just wait a little bit. After all, you're both well-education, independent adults. So use a little discretion and wait until you've tossed your graduation cap and earned your degree before you head out for a celebratory date-night together.