The cap shouldn’t be on when you are trying to bleed the system. I did the bleed procedure multiple times because I had made a mistake reassembling my pump after an engine swap.(plunger and spring were backwards) causing no flow. Having an assistant helps greatly because it’s hard to watch the reservoir and turn it lock to lock about 20 times with the engine running and cap off keeping fluid at the “min” bled it every time. With the fluid on the dipstick at the min level it shouldn’t overflow.
There is an unserviceable filter inside the reservoir as well. I also had a bad brand new “car quest” brand reservoir which some pieces inside were faulty/broken causing it to not flow properly. The adaptive drive itsa procedure may help some but I didn’t have any major air come out when I did the procedure.