"Head Bob" can be misleading. To me it means up & down and if that's what you did, left/right movement probably won't be detected. I move my head in a kind of circular fashion, like "around" the target and not N-S, E-W like the reticle. If the target/reticle move with relation to each other doing the circle thing, I know I've got parallax.
Parallax error can occur when the reticle does not lie on the focal plane. If you have a scope with adjustable parallax, you can use it to bring the focal plane coincident to the reticle.If you "bob" your head to the eye-box boundaries, both vertically and horizontally, you should see about equal error. If you only bob a small amount, it's possible to only detect it in one direction. It is possible to eliminate parallax by keeping your eye in the perfect center of the scope, but that is an iffy proposition.Ideally, minimum parallax occurs when the scope appears to be at it's clearest focus. But that is not always the case. You can play with the ocular adjustment as that might improve the parallax/focus agreement. When adjusting, best to do the head bob with the gun rested (hands off).
Left and right movement is what you need to be concerned with. When you see it you will know it. If you don't see left/right movement (parallax), note where your side focus/AO (whichever you've got) range to index dot is and give it a good twist. Then view through the eyepiece and test for left-right movement again. You should see some movement (parallax).You want to adjust the range until no movement is detected. That is a parallax free sight picture. You do have a scope with side focus or adjustable objective correct? If not you have a scope with fixed objective and preset range (fixed at one distance only). Whole different can of beans adjusting a fixed range scope..