I've had 100% success with this method:
If the bleeder screw is mangled from vise grips, etc. then grind it with an angle grinder until the hole in the middle of the screw is round and nicely centered.
Use a succession of left-hand drill bits of increasing size, centered on the hole. Use your judgment to avoid drilling too deep. Sooner or later, the bit will back out the screw.
Use a magnet and a Q-Tip to remove any stray shavings.
When buying a new bleeder screw, don't just eyeball it. Even within the same thread sizes there can be subtle differences in the angles of the sealing faces at the bottom of the screws. If you get the wrong angle, the screw will fit but it will leak. It's best to look up the proper screw by vehicle make, model, and year.
If you do manage to mess up the threads in the caliper (or cylinder) -- well, you haven't really lost anything because with the screw stuck in there you were looking at a new caliper anyway.