What word would you use for movement of 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 would use quivering.

I think it is hard to beat rustling but consider swaying or, more poetically, shivering.

Trembling