You can do the Bulgarian split squat while leaning your torso forward at about a 45-degree angle, which emphasizes the glutes and hamstrings, or while keeping your torso upright, which emphasizes the quads. This upgrade, however, applies to performing them with an upright torso.
Mid-Shin Height, Not Bench Height
Place your back foot on a surface that's around mid-shin height, which for most people requires a shorter platform than a weight bench. This prevents the possibility of overextending your lower-back and placing unwanted stress in that area.
The higher the surface you put your foot on, the greater the hip extension. And that hip extension range is steadily increased each time you lower your body down. Combine that with keeping your torso upright and you've got the high likelihood that you'll cap out of your available hip extension range of motion and be forced to have to overextend your lower-back in order to maintain an upright torso.
So with this variation it's less awkward to maintain the upright torso position and potentially safer on the lower back.