That's about it. I would make it as air tight as possible so the only air getting pulled is forced to go through the carbon. When I first saw your post I thought you had the PVC filled with carbon, so I drew these up. I guess I should have read more carefully. Anyway, here's how I would do it. It's the same as your diagram, pretty much just adding a coupler and an end cap.
You would cut a 4" hole in the center of the bucket lid, drill a bunch of 1/2" holes in both the PVC tube ad the bucket, then glue the vinyl mesh around the outside of the PVC and the inside of the bucket. Put the end cap on the tube, stick the top of the tube through the 4" hole in the lid, and secure it in place, in the bucket, with the coupler. Glue the fan, blowing up, into the coupler with the leads running out to a 12v wall transformer. Secure a sheet of 9" tall polyfiber around the entire outside of the bucket for a pre-filter, then fill the bucket up with the activated carbon.
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