One of the main items on the swarm check list is "growing room", or "laying room" for the queen. Can they continue to expand the brood nest and still have room to make more comb to store the food coming into the hive. When a colony fills their existing cavity and they have plenty of resources to continue growing, this is a trigger to swarm.
The queen gets put on a restricted diet to slim her down to flight weight and they start to develop her replacement by making "Swarm Cells ", essentially a baby queen nursery. (see link for images)
Within about a week, the mother queen and about 2/3s of the workers take off in one continuous motion forming a large cloud of bees. They may fly a few miles or only a few feet, but typically a couple hundred yards from the parent nest site until they find a resting spot. They form a cluster, usually on a branch about ten feet above ground, where they will rest and wait for the scout bees to locate a new nest site.
Scout bees begin reporting back to the cluster and recruit others to go investigate the site they have found. Using the "waggle dance" communication system, they direct others to the location and the process begins. They have a very organized system for voting and deciding on which site will be chosen. (See Tom Seeley's, Honey Bee Democracy, more details.)
They have been doing this successfully at a high rate for millions of years, or we would not still have honey bees today. However, the bees have been presented with a whole new set of challenges in last century that had lowered the percentages of success in there rate of reproduction.
There's obviously no way to know what these numbers are with feral hives, but studies have shown that in managed hives the donor colony is only successful and raising a new queen mother about 70% of the time.
The expansion of human populations takes away large portions of natural habitat and resources. With major forests and meadows of wildflowers giving way to farmland for monoculture and neighborhoods for housing, their ecosystems are shrinking. Not to mention all the roadways with high speed traffic and the invention and wide spread use of chemicals, many more obstacles for a queen on a mating flight to overcome than what they evolved with for millennia.
...more to come...