As Private says, it's all about your style. I own or have owned the 50mms (all Canon models other than the macro), both 85s, 100 f/2.8 IS macro, 135 f/2, and the 70-200 f/4IS and f/2.8 IS II. I have used all of them for headshots and here's my take.
The 50s are great for children and outdoor shots, with the 50L being best, followed by the 50 1.8 STM in my opinion.
The 85 f/1.8 is great for the money, but the 85L II is a stunning lens if you like to shoot between f/1.2 and f/4. If you shoot from f/2.8 or f/4 and up, i.e. in a studio, the 70-200 lenses are better choices. There's something about the 85L, though that works well for all portraits from full body to tight headshots that I love. It's a heavy, delicate beast, though, so it's not the most practical.
The 100L macro is my newest lens in this range and I'm starting to really love it for headshots because of the IS, close focus, bokeh, and sharpness.
The 135L is great for headshots, but if you use it indoors or in tight spots, it's not very flexible. The minimum focus (MFD) is a bit limiting as well compared to the 100L macro if you like tight shots. It's really light, which means you can shoot all day with it. It's probably the least flexible of all the options, but it also has a dreamy quality and if all you do is headshots, it's a great choice.
Both 70-200 IS lenses (f/4 and f/2.8 II) are excellent and highly flexible lenses for headshots. You lose the wide aperture and (being honest) some of the flaws that make the fast lenses so special, but for studio or any other kind of work where you don't need to blow out the background so much, they are excellent.
Based on my use, which is a mix of all techniques, I think I'd go for the 100mm macro, even though I've only had it for about 4 months. It's small, light, has killer IS, is fast (enough) for most work, and the ability to work without having to deal with a MFD makes it a joy to use.