It's pretty easy to do, especially if you use a nice convenient curve like Cos or Sin. The character controller even has a function for getting distance traveled (cc.velocity.magnitude).
So we can take these and scale them to make a function that adjusts the camera offset from the character controller to get a nice bobbing effect.
Which sounds like it would take about 10 minutes, but I confused myself about how character controllers work, read the documentation for the wrong method and then wasted an hour trying to figure out why my units were screwed up, when they were actually correct. Problem exists between mouse and keyboard.