Steve,
"Bronze" is part of the "Medalist System", which is a way of describing a level of proficiency. Within the Medalist System, there is Bronze, Silver, and Gold. Each of these levels is based on a syllabus of patterns, along with all associated technique. People use this system as a way of measuring their progress, and also as a placement system for entering into competitions.
If you are a beginning dancer, you are already working on your Bronze level, whether you know it or not. If you wish to become a fully "qualified" Bronze dancer, you should study with a school or teacher who will guide you through the process, teach from the syllabus, prepare you for and schedule your exams, etc. It is a very intensive but rewarding way to approach the learning process.
Some people prefer a more casual approach to learning to dance, which is just fine, too. Even people who don't actually take exams still like to use the syllabus as a measure of their progress, as well as a sort of a checklist of patterns learned. There's less pressure when there is no impending exam, but at the same time, there's less motivation to study and work hard. So for some people, testing through the medalist system is a very positive and rewarding experience, while for others, it takes all the joy out of dancing. Only you know whether taking exams is the right thing for you.
You can learn any dances you like, really. But there are four basic categories in which you can fully qualify:
International Standard (Waltz, Tango, Viennese Waltz, Foxtrot, Quickstep)
International Latin (Cha Cha, Samba, Rumba, Paso Doble, Jive)
American Smooth (Waltz, Tango, Foxtrot, Viennese Waltz)
American Rhythm (Cha Cha, Rumba, Swing, Bolero, Mambo)
The International style tends to be slightly more scholastically and/or competitively oriented, while the American style leans towards social dancing. But you can dance either style socially, and you can take exams or compete in either style as well.
You should realize however that American style, being based on social dancing, has no "official" syllabus, and every dance school you go to may have a slightly different set of steps from the last. All American style syllabi have a certain amount in common, but only to a point. International Style, on the other hand, has basically one officially recognized syllabus the world around. Wherever you go, people are dancing the same steps (at least at the syllabus levels). Plus, there is a very strong worldwide organization known as the ISTD (International Society of Teachers of Dancing) which governs the qualification process. So that makes a reasonably strong argument for learning International style if your goal is to become "officially qualified".
Or, looking at it another way, if the idea of working through the medalist system and taking exams appeals to you, then perhaps the International Style might be a good choice for you. On the other hand, if you prefer social dancing for casual recreation, you might prefer the American style.
You can download the Bronze syllabus from our website (www.ballroomdancers.com). We have step lists for almost all American and International style dances at the Bronze level.
I hope this helps. Good luck with your dancing, whatever you do!
Sincerely,
Jonathan Atkinson