Hello Worry!
Brave of you to venture out into a Web site like this and express your concern!
For many people dancing is more like a sport even though it looks like the couples are involved.
You don't want to constrain your girlfriend as that's an anti-pattern.
Try taking lessons for fun. It will help you to start understanding the culture and learn some cool new stuff!
Also, getting into dancing will desensitize you from jealousy. (I figure.) One way or the other it may change your life in ways that you can't predict.
On the other hand. In my humble opinion, there is concern for the fact that she isn't paying for her lessons. Never mind what kind of dance it is, I figure that this point of economics is the only issue to give thought too.
There is always a risk that she will find another gentleman (or you may find another lady) while she's doing her thing. Not any more with dancing than with any other sport or activity.
But the answer is to grow and not constrain or worry. Growing will increase your chances of getting what you want from life. Worrying will consume it!
Darcy
Darcy