You really don't need to close the oil tank filler plug, or screw, to bleed the pump. Just open the release valve and pump a few times. You are just priming the pump, which only involves removing any air from the oil galleries, not from the oil tank. The air that comes out when you open the plug, or filler screw, is not necessarily the air in the oil galleries, it is air pressure trapped in the oil tank and it is generated by the pumping action itself. That air pressure also builds up in the pump after you have used the jack a couple of times and sometimes even after one use. If a jack has worn O-rings, this air pressure can push the oil past these O-rings making a leaky pump.
Some jacks, like old Lincolns, Hein Werners and some Omegas, have breathers in the oil tank to prevent this air pressure build up. Sometimes this air pressure build up affects the performance of the pump so it is better to have it ventilated.
All jacks suffer more or less from this trapped air. The ideal situation would be to have breathers in all jacks, but manufacturers shy away from this because it would be an added cost since they would need to install a solid plug for the shipping of the jack from the manufacturer plant to its final destination, which would be the dealer selling it. They would also have to include the breather plug with the jack to be installed by the owner of the jack. And since many people never read the instructions, the breather plug would probably never get installed. So, a waste of money.
For anyone interested, a breather like the one shown below can be installed in the pump to ventilate it. The Yasui based and Torin pumps can't use this, or any other, tall breather plug in the actual place of the original plug since the handle yoke rests on top of the plug when the handle is in the vertical position. In this case, a new hole has to be drilled and tapped about an inch or inch and a half away from the actual oil fill hole. Jacks with universal joints don't have this problem as the handle yoke is asually away from the oil fill hole.