Leo - the answer is just practice and time at the crease.
Fast bowling tests not just your courage, but also your technique, if your technique is good and you are able to consistently able to "keep your shape" and play the ball under your eyes, you will be able to play it comfortably, once you have faced it and had time at the crease against it.
But this is the chicken and egg situation - if you are not used to it you get out quickly so don't get the time at the crease.
This is where the bowling machine is useful - cranking it up to mid 70's and shortening the distance it is coming from will allow you to get your feet going - but start with the machine in the 60's and gradually have the speed increased.
What you are actually doing is training your muscles to be used to moving a little faster. Actually this takes a surprisingly short amount of time.
If you don't have access to the bowling machine, then practice on a concete floor with a golf ball - Don Bradman style - throw the ball against the wall and practice your shots - the ball will spring off the wall and you have to move faster than you expect.
just mind the windows...!
Hope that helps.