How should one go about finding a reputable dance studio to take lessons at? Are there any governing organizations for ballroom studios?

Guest--

Yes, there are several governing org for ballroom. You didn't list your location, but I am assuming that you are in the US...you can look at webpages like:
usistd.org
ndca.org
usabda.org
bdf.org
Those are all "official" governing and rule making bodies for different areas of US ballroom. Some carry lists of professionals. In addition, you can check the lists of pros and studios on pages like ballroomdancers.com.

To be honest, a lot depends on where you are located. A large city will generally have several choices including franchised studios (ie. Arthur Murrays) and independent studios, and independent teachers. It is a buyer beware market. Every city is different. I would most often tend to suggest that you look through the local independent studios and teachers first...franchise studios generally cost more and some have high staff turnover. However, many franchise studios have excellent teachers as well. As I said, it just depends

Maybe respond w/ your location...I'll bet someone in the forum can help you...try placing a second post in the "In search of" forum, be sure to mention your location in the subject line...

When you are looking a studio, it is important that you have some idea of what you want to get out of your dance training. Then contact studios in your area to find which one offers the training that suits you best. If possible ask about trial lessons (or buy one) or about attending weekly dance parties to meet with other students. The latter is particularly important for social aspects of a studio experience.

If you happen to like the staff at a particular studio and how they treat you, you will likely be happy with the studio.

Blair