WELCOME ABOARD!
When the escorts are gunning for you, go deep (say 200 feet) and silent. If they find you, wait until you can hear them on an attack run. Go to flank speed, give it full rudder (direction doesn't matter) and drop at least 50 feet. This should help evade the depth charges. Once they're going off, go back to silent speed and creep back up far enough to give you room for a big depth change again.
It may take awhile, but patience is usually rewarded with survival.