A bridle horse, however, is a term reserved for horses very far along in their training. Moreso then just having a good handle on them, they can work a cow, will be an equal partner if one needs to get roped and held, and will be useful for any task on the ranch.
When a horse goes through the traditional progression of hackamore, two-rein (hackamore + bridle bit) and is ready to be ridden with just the bit itself, it's said to be "straight up in the bridle". If you ever see a mature horse in a bridle bit wearing an alamar knot around it's neck, this is why the rider has done so.
Now getting back to the fact that you see 2 yr olds in curb bits nowadays, there's a saying floating around that "there are lots of horses ridden in the bridle, but VERY few bridle horses". That's basically saying that you can hang a bridle bit on any horse, but few have really earned the right to do so according to the old ways. Most people I respect quote something in the order of 4-7 yrs before the horse is ready for this honor.
Hackamore with 5/8" bosal (bosal= bar 3/4"-1/2" diameter):
Hackamore with center-hung 3/8" bosalita (bosalita = bar < 1/2" diameter):
Spade bridle (bit with spoon + braces, Haener-made):
Two-rein step of hackamore+bit (should have rawhide reins...I had just finished the headstall but hadn't got the reins in yet):