The system pretty much self bleeds itself when the engine is running, if the fluid level is full and you cannot add anymore then the bleeding is done.

The airation of the fluid is another issue all together, you may have a loose fitting on the suction side of the system allowing air to enter. I'd recheck all connections , you also may have a faulty pump. I know you said it's new but doo doo happens.

Did you use and OEM part or go aftermarket ?

Aftermarket = No Good / Junk / Crizap, get the picture.