It sort of depends. Since this looks like it will mostly stick to the same formula, I'll say that you'll know you're facing a proper boss when a huge health bar appears on the bottom the screen, along with a name. These guys will never return. Then there are less identifiable sub bosses. In these cases, they might be characters in the world that are just tough as fuck to kill, or hulking beasts that are just tough as fuck to kill. If this stays similar to previous Souls games, the best way to tell which type these guys are is that they won't come back when you refresh the world.
But as for the true "boss" dudes, you'll know. They're generally gigantic, and like I said, they'll be a huge power bar across the bottom. And have fun when you stumble into one with a shit ton of souls...er...BLOOD ECHOS...and are just exploring, and you get you shit pushed in, and then have to make the stressful trek back to your death location in hopes of both beating the boss and getting your shit back.
Finally, glad you're liking it so far. The games are unique, despite the fact that this is the 4th one of their type. They have a huge learning curve and can really cause frustration, but they come with a sense of satisfaction that most modern games just don't have anymore.