Darn!
On behalf of beekeepers everywhere, I express my dismay that an exterminator was called and the bees (presumably) destroyed. Next time that happens, get hold of a beekeeper, who will come and put the swarm gently into a container, and will then have 30,000 free bees to take home.
I believe that most, if not all, beekeepers are happy to go out and rescue swarming bees, if for no other reason than to educate the public a little bit about bees.
The local county extension service would have been able to recommend the names of several local beekeepers. Beekeeping may e just a hobby for most people, but for a few people it is a billion-dollar a year industry–these folks keep hundreds of beehives, and truck them all over the country to pollinate big agricultural crops like orchards and blueberries, following the seasons.
Darn! Double darn! What a waste. 
As to what the bees were doing, bees swarm whenever they outgrow their living quarters, especially in the spring. Like Jophiel said, they raise up a new queen and then half the hive splits off and follows her. During the time that they’re hanging in a tree as a swarm, they are actually relatively calm, because they are still deciding where to go. (They send out scouts.) So it’s fairly easy to collect them. It doesn’t even have to be a regular beehive. Beekeepers have been known to gather the swarm into a hat and carry it home and pop it into a hive.
In the olden days, finding a bee swarm was a great event, “finders keepers”. They’d take it home and put in into a “bee gum”, which was a section of black locust tree log. Or into a woven straw beehive called a “skep”.
But I suppose the school was worried about somebody being stung and suing them…Darn!

“Why, sometimes I’ve believed as many as six impossible things before breakfast!” - the White Queen