The Bulgarian squat was developedand used in the old eastern block (including Russia/Hungry) by Olympic lifting coaches, as far as I know. It highlights the glutes and hams, as well as the thighs. The knee was not to go beyond the plain of the toes. In other words, it was a learning exercise as well as a strength movement. And because using one leg at a time made sure that the total leg/hip/hams shared equal development and strength with the other leg. Step-ups, a similar exercise but not exploiting the same exact function of the Burgarian squat, is another eastern block developed movement. Doing either will aid the regular squating power strongly. (Just to mention, a one legged squat is not the same as a step-up. The working legs is usually along side the body while doing that exercise rather than in front when doing Bulgarian squats or step-ups)
With the Bulgarian squat, the extra weight is usually held in front of the body. Some will just hold a BB plate/DB near the chest area. Or very advanced men will hold a BB, as if doing a front squat. The step-up is usually done with the BB resting on the neck like in a regular squat. In either case DB's can be used in both exercises, though the dynamics will change a bit. BB'ers might pay attention to working each leg one at a time in regular leg training. This can insure equal balance and leg development. Good Luck.
