Watch Dr. PP vs. Mew2king. In almost all of their sets there are points where M2K stays on the ledge for a little, and PP does a great job of dealing with it. The main things I would recommend are:
1. Stay patient. Simply waiting a little makes you less predictable. If you always wait 2-3 seconds and then go for the ledge, it makes it super easy for him to LH and smack you away. You have the advantage, so just take your time and be as safe as possible.
2. Watch their patterns. People who regrab the ledge will have a pattern of some sort. They may mix up their timings, but ultimately there isn't a single timing that they can always use. They have to adjust when they regrab for invinc based on where you are. Once you know how they will react to a certain movement that you do, you can abuse it by baiting an attack and hitting them or making them feel safe about regrabbing and then WD onto the ledge before them.
3. Use your shield. Shielding is the best and simplest bait you can do when they are just LHing attacks every time you get close. If it's Sheik, for example, you simply WD towards her, she reacts by LH fairing, and then you just bair OoS. If they know you will shield and just try to regrab, that would be your chance to grab the ledge. Again, don't feel like you have to do this right away. Simply staying close to them when they're on the ledge puts on a lot of pressure even if you can't tell by their actions. They have to maintain constant concentration in order to stay on the ledge, and they are bound to be baited or fail to attack at the proper time eventually.