Has anyone noticed on their AR-15, when they pull the trigger, there is a tiny bit of "pull-back" movement from the trigger before it breaks? This is what happens on my 20" Bushmaster AR.

It is kind of difficult to explain but there is a small amount of movement of the trigger moving toward you when shooting. The trigger pulls back maybe 1/8" and then holds until enough pressure is placed on it that it breaks and sends the round downrange.

Is this movement normal on an AR-15 stock trigger?

That's called take-up, it is normal on all firearm triggers.  Proper take up allows for easier bench shooting, as you can take out the slack and be a little surprised by the break, helping to eliminate flinch.

If you had to immediately apply full force with your finger when firing, instead of your finger ramping up the force as the trigger moves, you would jerk the trigger more easily and throw more shots.

Perfectly normal.

Sounds about right for a stock trigger. I always like the gritty feel of a brand new fire control group in a fresh built rifle. That means it needs to be shot more to smooth out the action.

If you cannot get the "feel" of it, you can always try to switch it out for a RRA Two Stage Trigger.

It is a little thing called creep.  It is genreally not considered a good thing because it is not a consistent take up  like a 2 stage trigger.  Funny the last couple Bushies I sold at my shop had great single stage triggers with no creep at all.  Now the DPMS that I just sold, that's another story........