Say there's a small animal hidden among bushes and it causes the branches (if they can be called that) of the bushes to shake/move slightly. Now the sound of this could probably be described using rustling, but what word would use to describe the visual shaking/movement of the bushes?
According to the Free Dictionary, you have it backwards: rustling refers to the movement, and the sound is thus implied. Personally I associate the word so strongly with both the movement and the sound that I would use it for either meaning.
So, stick with rustling.
To add to the other answers, a simple accurate word: shaking.
Suppose the small animal happens to be a tortoise, the bushes might slowly flex as the tortoise lumbers between them.
Now suppose the animal is Tasmanian Devil, the bushes might flap violently as the Devil rushes through.
If a breeze is blowing the bushes might rustle.
I think it is hard to beat rustling but consider swaying or, more poetically, shivering.
I would use quivering.
Thinking of the rigidity of bushes I would fall on shudder; it fits well with the shape of the object.
Shudder also implies a geometric uneasiness, and pins and needles. A part of your question (the movement/sound of a leaf) is answered by rustling; shudder is complementary as it pushes further into the character of bushes or shrubbery, and moves away from trees and more pliant plants.