How to bleed a power steering pump
What I do is to remove the belt and use an air wrench with an Allen adapter to manually spin the PS pump. Watch the reservoir for bubbles. STOP once bubbles are seen. Wait for the bubble to settle and repeat.
Using a tool to spin the pump also helps because it is not spinng as fast as the motor would spin it.
When no more bubbles are seen using the the tool, reattach the belt and start the motor. STOP as soon as bubbles are seen. Wait for the bubbles to settle. Repeat unitl no bubbles.
Doing this with the front wheels off the ground will reduce the pressure and thus make it easier. For cars with a hydroboost system (Mustangs), it will be necessary to work the brakes as well.
DO NOT run the pump backwards.
As I stated before, once bubbles form, continued running will just make the bubbles smaller. In effect homogenizing the bubbles into the fluid. While I can't say for certain if the pump is bad, I can say that once tiny bubbles are in the fluid it can be very difficult to get them all out.
Since you have stated running it for 3 hours, likely there are very tiny bubbles throughout the system. You should be able to get them out but it will take some patience.