I'm making a music video and in a section of it I want to have a circle bounce, in time to the music, off the sides of the composition. When the circle hits the sides of the composition I need it to contract, or squeeze, like a real ball.
I'm aware of the "Squeeze" option in the built "Warp" effect, however, I've found this quite tedious and not very flexible.
I was wondering if anybody could recommend a more flexible feature or approach to achieving this effect?
Not sure what you're asking. Some things take time and are labor intense and if it means animating things with lots of keyframes, then that's how it's got to be. You can ask any character animator of whatever you consider your favorite 3D animated movie about that and they'd give you some weird looks because you call 50 keyframes a tedious job when the deal with thousands of them on every single shot. Sometimes there are no easy solutions. If you're concerned about the look of you squeeze, then I'm sure you can substitute or complement your effects e.g. with Liquify, Mesh Warp, the Puppet Tool, Bezier Warp and others.
If you mean that you want it to squash and stretch as it bounces, then you can grab hold of one of the little squares around the circle while using the selection tool. If you know Photoshop, then grabing the little squares is like using the free transform tool in Photoshop.