Bridge press is an advanced move done by Russian powerlifters.
The Russians perform the bench press like a supine push press. They figure if the feet HAVE to stay on the floor, you may as well initiate the lift from the floor.
They push hard with the feet like a push press, with tension rising through the body till it gets to the upper back.
The bridge press is an excellent assistance exercise if you press in this fashion.
The Russians do no assistance work till they can bench 140kg.....simply coz its not needed.
The bum simply "brushes" the bench, the arch is high, you are resting on your upper back and feet.
This builds little in the way of muscles and true pressing strength.
Like they say, they dont want to get stronger, they just want to bench more.
They generally have programs for either competetive or non competetive lifters, very different.