Good explanation. I would add that on some installations, the manual prime pump is mounted on the secondary filter, and the bleed "screw" is a pass-through with a nipple on the top much like the bleed valve on a brake caliper. What works for me is to put a short piece of tubing, 18 to 24 inches, (I use clear vinyl tubing; think aquarium air lines) on the nipple and with the wrench on the screw body first and run the tube into a clear bottle or jar. This way as you pump you can see when the discharge is clear fuel indicating the air is out of the filter. It may drip a little around the bleed screw threads, but much less mess that just using a rag. Tighten the screw and a few more pumps (Note: my engine does not have a fuel supply pump) until resistance is felt and it should take right off. There is no unfiltered fuel introduced this way.
One other thing, remember to turn the fuel line valve off before starting the filter change and to turn it back on before bleeding. It is possible you could siphon fuel from a fairly full fuel tank, and obviously it won't prime if the valve is off.
