The catcher must cross their hands over before they catch you. Catch their crossed hands and keep your legs together. You will automatically turn in their arms to face the platform as you swing (one arm will be twisted). In the apron, lift your feet up and place them on the catcher's biceps. Push your butt through and make a Bird's Nest position (again, this will feel odd because one arm is twisted). At the peak, let go of the catcher and grab the fly bar.
You can find out more about this trick in my books: