Separation anxiety is something that all children go through - when they realize that they can move, they realize that you can move too, and that you might go away and not come back. The wonder isn't so much that children go through separation anxiety so much as that separation isn't worse than it is.
Of course, when dealing with an autistic child, separation anxiety is worse than with a neurotypical child, and extends to a much older age. Case in point: Yesterday Mrs. B. had to wait for the school bus with Little Boy B, age 7. Not only was he waiting for the bus with someone other than me (strike 1), he was also wearing a new pair of shoes (strike 2), and Mrs. B., being not dressed appropriately for the cold, tried to get him to go down the front walk to the bus by himself (strike 3). Result: Meltdown. This morning I was back on morning bus duty. He's gotten used to his new shoes (mostly), and so the transition went smoothly. I convinced him to try walking halfway to the bus with me and then halfway by himself, and he managed that without a hitch, so I'd consider today's transition a major success. Of course, the real test will come tomorrow, when Mrs. B. is back on bus duty.
It any of you are having trouble with separation anxiety, here's a list of tips from St. David's Center for Child and Family Development that can help out.