Sounds like a shoulder flexibility issue if you can both go back and stand back up on one leg. If your wrist elbows and shoulders are not in a straight line perpendicular to the floor in your bridge, your weight will stay too far back when you kick. Inst
of the majority of your weight being in your arms, its in your hips and you fall on your back.
Trying to kick as soon as your hands hit the floor can be dangerous if you are just learning the skill. If you miss it and your hands and feet are off the ground at the same time (essentially jumping into the walkover) you can injure your elbow. I have personally seen this happen twice. It is common in people who lack shoulder flexibility because they instinctively want to "jump past" that flexibility barrier. A BWO should be one SLOW smooth continuous motion when first learning it, you can speed it up AFTER you master the skill.
CP got past her terrible shoulder flexibility by bridging with her hands on the floor next to a wall and pushing through her chest to touch the wall, slowly increasing the amount of time she held it for, along with having a coach seal stretch her, and stretch her over his back.