I coach at a high school in town and we pile up mats,depending on how tall the gymnast is, make them kick up into a handstand with the back flat on those piled mats. Then make them fall to the bridge. Gradually take mats away and its less of a shock factor when their feet are falling all that way. Hope this helps!
More than drills, I've found that you need to have VERY good shoulder and upper back flexibility, or you get that bent kneed, legs apart, on their toes, shoulders moving forward, bent arm sort of thing. All my girls that can do that skill well are able to put their hands at the base of a wall in a bridge and push up in perfect form and have their chests flat against the wall. It takes time and work to get the amount of flexibility, but when you do, you will find it pays off in many other skills as well. Keep at it, and good luck.
Have the work them onto a resi mat. They should show a balanced handstand position and slowly move into a shoulder and upper back arch that they can control through the first 1/3 of the distance to the resi. Have them work it like that until they can land gently on the resi, and they have them add a reversal that goes back up to the handstand position.
If they can't make that work after a few practices it's because they need more shoulder and upper back flexibility, and should work on that for a few weeks before going back to the limber work. Measuring progress isn't as simple as going from not having a skill to being able to do it, so measure progress by how hard they're working on what it takes to make the skill work.
Thank you all so much!! I used your suggestions and it worked. I didn't even need to do the piling up mats. I had them do handstand, reverse plank and held their feet in that position so that they could feel the position and that their shoulders should not move forward. Most of them improved significantly and are able to do it now. A couple still need a little more shoulder flexibility, so I've incorporated bridge with chest pushed back to mat or against wall holds into our stretching routine.