It is a somewhat simplistic view because light isn't just a particle bouncing off walls, its a wave. What happens is that the fiber creates a 'waveguide'. This

It is a somewhat simplistic view because light isn't just a particle bouncing off walls, its a wave. What happens is that the fiber creates a 'waveguide'. This will gently curve the wavefront around the fiber. I barely understand this myself. But the way I imagine this is essentially as a water wave running through a trough. Lets consider a simple sinusoidal wave originating at one end of the trough. Lets call a wavefront any line across the trough that follows the peak of a wave (really it can be any fixed phase, but peaks are nicer to visualize). What happens to these wavefronts as time goes on? They bend around the corners. Essentially the water just in front of the wavefront is going to be pushed up next, and when this happens has a lot more to do with distance from the current wavefront than whether the actual water particles are bouncing off the wall or not. My explanation of wavefronts moving forward doesn't quite explain why the wavefront 'rotates' in a curved waveguide. I would guess something about path interference being different on the inside of a corner than the outside. Someone who actually studied this stuff probably knows a lot better.