The issue with your PSD isn't with the bevel, it's with the shape. Without the bevel, the shape is very pixelated to begin with. Here's a few pointers. When using any form of selection tool whether it be marquee, lasso, or pen, always make sure you have anti-alias enabled.
Secondly, when applying bevels, try to avoid using the chissel options, they're actually intended to look rough which can cause the illusion of pixelation even on the smoothest of edges. If you wish to have a hard bevel, use the Smooth option, but increase the Depth accordingly, as this will harden up the edge the more you increase it without pixelating.
There is a very good method to smooth out any pixelated edge, but for now, I will just send you a modification of your PSD wih a smooth shape and bevel. If you still wish to know how it's done, I will write a short tutorial.
Here's a link to the PSD:
Download
Peace, Lance