In an ant (or bee) colony, what is the very approximate ratio of new breeders to workers?
So.

This answer is specific to the western honeybee, Apis mellifera, as there are massive amounts of data on them; more, possibly, than any other insect species. There has certainly been more data collected about them than any other hymenopteran.

At around the time of the nuptial flight, there may be as many as 60,000 workers in the hive, though likely number is more like 15,000 - 20,000. There will be either one (virgin) or two (one mated, one virgin) queens (the old queen will stay with the hive, if she is alive). There may be as many as 400 drones from the original colony (though usually the number is less, around 150 is typical; 10 - 50 of them will actually mate with the queen), and an equal number may join in the flight drawn from other colonies, especially in commercial beekeeping operations. Somewhere between 1000 - 6000 workers will take part in the nuptial flight with the virgin queen and the drones.

This means that in honeybees, the nuptial flight contains 1 queen:~5000 workers:~150 drones.

Data is drawn from many years working with bees and beekeepers. Opinions will vary somewhat depending on the beekeeper and the beekeeping methods. These are based, generally, on bees kept for clover and fruit pollination in the western USA.