I couldn't help but add this --

You don't "steer" the bike with the handlebars. The only time you need to do this is probably while standing on the ground, off the saddle, while you maneuver the bike in & out of your garage or at an intersection or bike rack.

It really is about weight transfer and looking where you want to go. You'd need to become UNaware of the phrase "weight transfer", though. Just look ahead, lean your body, and go.

Your body's own balancing reactions are the result of millions of years of evolution. It's all automatic. Don't think too much. Let go, Luke.