Hey George, another good topic.
The timing necessary to run from the right side to the left side is not nearly as precise as the final move up the ladder, but on Level 4+ you can STILL get whacked if you do it wrong and a bad combo of springs occurs.
The short answer is that you want to wait for a short or at least a medium / short spring to come your way before dashing to the left -- this gives you a chance to begin your move earlier and be positioned closer to Pauline's ladder as the spring passes over your head. One tip here is that the first safe spot is at the top of the ladder, but it ALSO includes about one step to the left. I used to notice that Dave probably takes the most advantage of this, taking a large step to the left and stopping before looking at the springs. This is another thing that you should use a save state for -- position yourself at different places one pixel at a time and truely learn where the safe spots are more precisely. But, I'll say that you can easily take a step left and stop in a position that puts the right edge of Jumpman's body tangent to the left edge of the ladder which you just climbed and you'll definitely still be safe.
From there, you can begin running about half way to Pauline's ladder before a short spring bounces over your head -- if you get this good of a Jump and you began on a short spring, you will ALWAYS make it to the 2nd safe spot, there will never be any need to retreat. However, if you get aggressive and try going on a long spring or if you feel like you got a terrible jump, you can technically "retreat" back to the first safe spot if you spot another short spring coming and you're afraid you won't make it -- you don't usually see players doing this because if you get even a reasonably decent jump you won't have to retreat, but it's always an option.
The key, just like with the final approach, is getting a good jump -- and many novice / intermediate level players actually play it a little too safe by avoiding contact with the spring in both cases. Remember that if the bottom of a spring bounces up and hits you in the face, you generally survive because of how the collision detection works so you need to learn to take advantage of this and get better jumps in both directions.
(Since this is the Basic Strategy, I'll leave it there for this topic, but in general I now firmly believe that "timing" a "jump" in either direction is the vastly inferior approach to the Elevator screens -- I personally use techniques that lean much more heavily on "positioning" rather than "timing". Perhaps I'll expand upon that in the Advanced Strategy section at some point.)
