There does not appear to be any way to increase the chance of rustling grass, or the water/cave equivalents rippling water and dust cloud. They seem to occur after an unknown number of steps have been walked, and they only seem to appear on the current screen when this number of steps has occurred.
Every time you take a step, there is a small percent chance that an on-screen patch of grass will start shaking. Knowing this, if you run back and forth next to some tall grass, it won't be long before a patch of rustling grass containing a rare Pokémon will appear.
It's like Hidden Grottos resetting (or at least having a chance to) after 256 steps. When a certain amount of steps are taken, the grass resets and has a chance to produce rustling grass.
It's unclear how many steps determine the reoccurrence of a phenomenon, since you can see a rustling patch of grass just after you've finished a battle in the previous patch. It could perhaps have something to do with the time spent in the same patch of grass, since from my experience, the longer I've stayed in the same place, the less encounters I've had with phenomenons.
Phenomenons also happen in the vicinity of your player character, since there is a radius of about 5 steps where the phenomenon will appear, so the chances of you getting rustling grass while actually in the grass patch is larger since you're surrounded by more grass.
This is all speculation though; there isn't a specific number that I can find, as there is for Hidden Grottos.
However, it has to do with taking a certain amount of steps, since if you stood absolutely still and left the game on, no phenomenon will appear.