For a long time, I had no idea there were kicks in the Shoulder Bridge. I would just roll my hips up and roll my hips down. And, all the while my feet were moving around and my knees would open up more. I was skipping so much of the good stuff. When you do your Shoulder Bridge be mindful of equal weight on your feet front to back and side to side. The more you can connect to your inner thighs and your outer thighs the more stable you'll be. Then when you do add the kicks in it will be a piece of cake!
Try transitioning from High Bicycle into Shoulder Bridge with no sound.
Traditionally done after High Bicycle you'll see in this video that I just get into my Shoulder Bridge from Neck Pull. You can do exactly as I did it, especially if you are not doing High Bicycle. Or, you can get a little fancy and turn your hands sideways in your high bicycle. Reach on or both legs out, bend the knee/s and then lift your hips as your feet land on the mat. If possible leave your hands under your hips. The hands are not for you to rest your seat but instead to help encourage your hips higher and allow you to feel if your hips drop throughout the movement. It's also a great chest and shoulder prep for Rocker.
Once in position slide one leg out and point the foot to lift it up. Then flex the foot and press the leg down. You can lower the leg as much as you do not drop your hip. Repeat the lifts and lowers 3-5x on each side. Then remove both hands and lower yourself down with control. I like to use these kicks to prep me for my Side Kicks.