This paper puts the introduction of the European honeybee into the Americas in the 16th century.
http://biology.usgs.gov/s+t/noframe/x189.htmI am by no means a bee expert and appreciate the information about survivors of bee stings. My interest in the subject came as part of a project to restore my suburban yard to a more natural state. The first step was to inventory all native and introduced species. This is when I learned such familiar friends as the European honeybee was an introduced species and that virtually every plant species in my yard except Poison Ivy and Trumpetcreeper was also introduced. Yikes. I have revised my dream and decided not to be a purist in this matter. Honeybees are discouraged only in so far as they are actually disturbing my native hummingbirds -- and fortunately I have discovered that my hummingbirds have been able to hold their own just fine despite occasional visits from the bees.
Anyway, my native pollinators include Bumblebees, Yellow jackets, and (I hope but at this point I'm not all that sure!) various wasps I can't yet identify. The pollinators I make the most effort to attract are the hummingbirds. In that, I have been very pleased and pleasantly surprised at the huge numbers of hummingbirds that will move through a yard planted to attract them. Many come with a thick coating of pollen on their head, it's pretty funny at times.
My hope is that if the honeybee proves to be a short term (in geologic terms) visitor to the Americas that our native pollinators can step up to the plate and take up the slack. The article I cite, however, points out the enormous economic value of the European honeybee and it does sound as if there could be tremendous problems if it were to disappear.
The more I learn about my area, the more I realize that if I were to be dropped in my neighborhood as it was 500 years ago, it would seem a very alien place with many unfamiliar species and many "missing" species.