Like Maurer said, keeping your line out of the water is crucial, not just for setting the hook but also for getting a good drift.
I would recommend focusing on lifting your rod (directly up or downstream or whatever direction is safe) rather than cocking it back by bending your elbow. That will help keep you from whipping your line into trees.
You will also be a bit faster if you hold your line in your free hand and give it a tug at the same time that you lift your rod.
I got no style, I'm strictly roots.