So how is that any different? How do you know your local Bible study leader, if the RC has one, is right in what they’re teaching?
Who's "we"? If you mean "Catholic laypeople," you're quite wrong. In fact, private Bible reading is an indulgenced act, and has been for a long time. The Church can't promote anything more highly than to attach an indulgence to it.
Only Rome can tell us what is or isn’t right.
Wrong. God didn't give you a conscience as a vestigial organ. It's your duty to form your conscience by studying correct teaching, among other things. Sitting around waiting for Rome to rule on every jot and tittle will keep you waiting for a very long time.
It's been 2000 years, eagleone. Most question have been posed before, most of the answers, with varying degrees of authority, are written down in books. Much of it is even on the Internet. If I had trouble understanding something or it seemed contradictory, it's not that hard for me to find a solid priest and ask him.
Your question is a little bit like asking how anyone do mathematics without the International Mathematics Union issuing an authoritative decree that every line of every solution to every problem is correct. If you're just trying to compute how much fertilizer you need for your lawn, you don't really need to go to the world's highest authority on math to figure it out.
How do you know your local Bible study leader, if the RC has one, is right in what they’re teaching?
I don't go to parish lay-led Bible studies, because they're usually really bad. (Not goring any individual ox here; I'm just speaking generally, in my experience ...) As I say, if I have a question, the answer is usually written down (I have a fairly big bookshelf) or on the Internet.