In my case the pump regulator is very sensitive to engine vibrations and the vibrations seem to cause the gasoline to vaporize and that looks like air bubbles but it is really gas vapor bubbles. So if you look at my engines the pump regulator sits on a foam padded shelf and is loosely held in place with a length of Velcro tape. That isolates it from the engine vibration fairly well and then the pump regulator tends to work well. 

The other caveat is you have to work the pump around at different angles to get the air bubbles inside out of it. I usually move the plane around at different angles working the air bubbles out. I usually only need to do this for the first engine run of the day, after that it is filled up with fuel good and no air in the cavities inside.  But I also started using a third fill line to the fuel tank so I don't disturb the fuel line itself and introduce air bubbles in it while refueling the plane. These pesky air bubbles from when the pump regulator is empty at first and filling up as the engine is runnign can be a hassle sometimes.

Now several people have run the engines without a pump regulator. We actually have one fellow at our club field who is doing just that same thing too. Unless it is on a test stand, you really need at least muffler pressure for flying in a airplane.  I also think a couple of guys used the Cline regulator along with a Perry pump too.