When the angels had left them and gone into heaven, the shepherds said to one another, "Let us go now to Bethlehem and see this thing that has taken place, which the Lord has made known to us." So they went with haste and found Mary and Joseph, and the child lying in the manger. When they saw this they made known what had been told them about this child; and all who heard it were amazed at what the shepherds told them. But Mary treasured all these words and pondered them in her heart. The shepherds returned, glorifying and praising God for all they had heard and seen, as it had been told them.
They had to check it out, of course.
The angels had made the big announcement to them, and given them a "sign" to know that they were in the right place, so of course they had to go check out what his thing was that the angels had announced, what the Lord had revealed to them.
I've always wondered what became of the sheep. Some of the songs of the season suggest that they simply left the sheep behind. This would be a fairly serious thing; to the owners of the sheep it's quite likely that the sheep were of more value than the shepherds. Was one poor sap left behind to stay with the sheep? Would one be enough, given that the sheep were quite likely agitated after that interruption from the angels?
I like to think that they herded the sheep along with them. After all, this child was lying in a manger. If there was a manger around there was probably food as well as possibly shelter for the sheep. As a result, I imagine a pretty crowded scene around Mary and Joseph and the child Jesus, with the shepherds and sheep crowding in along with whatever other animals were already there. I like to imagine it, but of course I have no evidence for it.
Whatever became of the sheep, the shepherds made their way towards Bethlehem, and did so "with haste." It doesn't say "they ran." Maybe the sheep were slowing them down. But they got there as fast as they could, in plenty of time for a heaping helping of cognitive dissonance.
It's not like they weren't warned. The angel was pretty clear about what they'd see; a child lying in a manger. Still, it wasn't as if the medium and method by which the message was delivered truly prepared them for such a humble sight.
Most scholars suggest that the manger was found not in the rustic kind of stable we imagine, but in something more like a man-made cave, hewn out of rock; in other words, something not far from a literal hole in the wall. Inside were the child, still rather newborn-looking, probably squawling a bit (NOTE: I'm told by those who have given birth to children that if you're newborn child doesn't cry there's a decent chance something is wrong; that rather stupid line in "Away In a Manger" about "little Lord Jesus, no crying he makes" is absolute BS, nothing more than an attempt to shame Victorian children into being little pod people); Mary most likely spent and wiped out from giving birth, and Joseph in whatever state of panic he had achieved by this time. It's hard to imagine that the scene itself wasn't quite what these shepherds imagined after all that angel stuff.
Whatever dissonance there may have been, the shepherds didn't seem to be deterred; they unloaded their whole story on Mary and Joseph. Luke makes it sound like there were others on the scene as well -- "and all who heard it were amazed..." (emphasis mine) -- maybe the keeper of the inn? Maybe the innkeeper's wife? (As played by Pig-Pen and Frieda in "A Charlie Brown Christmas," perhaps?) In any case, we get x number of people being amazed, but Mary starting her own My First Baby Book in her own memory.
Certainly Mary hadn't completely forgotten the announcement from the angel Gabriel, or perhaps the experience of that crazy prophetic song coming upon her from out of nowhere when she was visiting Elizabeth. At the same time, though, the girl was tired. She could really have used some rest. But the shepherds crashing in (with or without sheep) no doubt brought back to her all of the unbelievable and awe-full things that had led up to this birth, providing a reminder: remember who this child is, Mary; remember who this child will be. And the shepherds' account of the angelic announcement brought back into sharp relief for Mary just what it was to be the θεοτὁκος.
As for the shepherds, they were presumably polite enough not to overstay their welcome. And they ... returned. To their fields? To their sheep? To that one schlub left behind to keep the sheep? To an empty field deserted by the sheep who had wandered off and gotten swept away in a nearby river? We don't know. They disappear from the story. But they disappear "glorifying and praising God for all they had heard and seen." Maybe that made the nights alone with the sheep easier to bear.