That's a tough one. Without calling your local water department, it'll be hard to know 100% for sure if you've got hard water or not. Here's a map of water in the US, just to give you an idea:
It's obviously not exact, since different watersheds may have different qualities. But this may give you a broad idea.
Welcome. Be really careful with Dr. Bronner's, though. It's a castile soap. So if you have hard water, it will not rinse out well in it