This is likely to be your experience.: You will line up for quite some time in the Basilica of the Nativity with a very large number of other people as you inch slowly closer to a series of narrow, steep steps down to the grotto.
In the grotto you will experience a stuffy atmosphere in a small confine with everybody jostling to experience a few seconds under the curtain at the main alter before being directed out. It will not be a peaceful experience.
That was our experience but we were fortunate enough to be staying nearby and went again the next morning at 5:30am and experienced the grotto with only a few others (and no line to get in) and were delighted to be part of a mass in the grotto with an Italian group of about 20. A very peaceful, contemplative experience.
My tip: go early!