AIOs should be washed about the same number of times as a regular diaper. I believe the AIOs are white (bleached) though so that would mean about 2-3 washes should do it, as opposed to unbleached which would need 4-6. They'll probably keep getting a little more absorbant for a couple more washes after that but they should be ready to use by then.
And yes, just once for covers is fine. For the diapers you're washing out the natural oils that interfere with absorption but for covers you're only getting rid of any dust or manufacturing residue.