The instructions don't mention drilling pilot holes on the bottom of the shelf. What size bit should I use?

A 5/32-inch drill bit should do the trick but double check its size against the screws to confirm it is not larger than the root of the screw (the center core just below the threads). It is also a good idea to put a piece of tape on your drill bit at approximately 5/8-inch to indicate the depth of the pilot hole so you don’t drill further into the workbench.