A bridge rectifier is just the term used when a collection of diodes is arranged in a particular way. As compared to a single diode.
The CL alternator is a single phase alternator, as mentioned, which means that it only has one phase, or circuit, creating the AC power. Other bikes use a three phase alternator, which has 3 separate phases, or circuits, creating the AC power.
Here's a schematic I drew up once for a Honda SL125 circuit. Pay no attention to the lower half of the diagram - the bridge rectifier is the upper half, showing the four diodes. AC flows on the yellow and pink wires from the alternator. The 'rectified' output, or DC, flows out the red wire to the battery & load.
BTW, thanks for that link to the great plains site. I ordered a few of those bridges just today. Working on a couple projects where they'll be needed... Thanks.
Kirk