Counterbores typically have two dimensions: The OD of the cutter, and then the "pilot" od, which should correspond to the ID of your bearing, or more specifically, to the OD of your pivot hole. Pilots also have "stems" which fit into the "pilot hole" on your counter bore. Depending on the size of the counterbore, the pilot hole might be 1/8, 5/32, 3/16 etc....
A lot of times you can just buy your counterbore set up with the proper cutter OD and a corresponding pilot, but if you need a specific pilot size, and/or you already have a cutter, the pilots can be bought seperately. If you have a lathe, you can make your own, or turn one down as needed.
For caged bearings, the OD doesn't have to be super precise, and can run a little larger if necessary, as the pivot will keep the bearing from moving side to side.