You can train yourself to pick up the curve ball earlier and more automatically -- reacting without having to think consciously.
Start by watching the pitcher during his warmups and when others are batting. Pick up how his delivery differs with different pitches. In the case of a curve, his arm action has to differ from his fastball. Some disguise it better than others, but at some point you will at a minimum pick up a different hand position at release. This is your cue to stay back and also not to bail if the pitch at first appears inside.
I am constantly amazed at how many young players never think to watch the pitcher until they're in the batter's box. In addition to picking up on mechanical nuances, you can also often discern the pitcher's preferred patterns. This will help you to know when you are most likely to get a curve based on the ball/strike count.
You can also work hand toss drills with a partner to aid in pitch recognition and staying back. Start by having your partner change spins on the tosses. You have to call out the pitch before you swing.
Next, have your partner toss you some the normal way, then randomly toss some to you on a bounce with you hitting the balls on their way back up from the ground. This forces you to watch, adjust, stay back, and still be in a position to drive the ball.
In the end, a good curve ball is tough to hit. That's why pitchers throw them! But with recognition, you can at least avoid chasing balls out of the zone, and be prepared for the hangers. If you get to where you can hit a good curve ball, you will be on your way to some big numbers.
Also bear in mind that they give you three strikes. You don't have to swing at the first thing you see. Some pitchers will throw you repeated breaking pitches, but in most at bats you will get at least one fastball in the zone. For the most part, you can succeed if you focus on waiting for that pitch and nailing it. Your curve ball approach can be used as a 2-strike approach if you wish to wait deep into your at bats.