I do d1 and in between the animation roll my thumb to down-back, wait a fraction of a second (watch for Bane's leg start to retract) and then press f3.
If you hit with d1 it's +17 so body press comes out in 3 frames so unless they do something unthrowable they get scooped.
If they block d1, it's +3 so they have 17 frames to do something before body press comes out, but if you're juiced then they get scooped.
So pretty much the only way to get out of it is to block the d1 and do a throw invincible move or jump.