It takes a long time to get all of the air through just by pumping the pedal, and only a small amount of air makes a lot of difference.
One problem with pumping the pedal is that when you release the pedal, the air bubbles get sucked back in. If you don't have a non return valve or a vacuum pump, then you need to press the pedal, open the bleed valve, watch the bubbles come out, close the valve, release the pedal. Repeat this ad nauseum remembering to keep the reservoir topped up. If the system sucks air from an empty reservoir, you have to start all over again.
The air will only be able to come out at the bleed valve if the fluid is flowing in that direction. If the fluid isn't flowing, then the air can still go back through the brake lines. So closing the bleed valve, pressing the pedal and opening the valve needs to be done without undue delay - simply to keep the fluid flowing towards the valve. It helps to have a closed ring spanner on the bleed valve, so that you don't have to reposition it every time.
You have got pads in, haven't you? You aren't just pushing the pistons out as you pump the pedal ?