Jamie
No need to panic. The term "Killer Bees" was coined by the media. The proper term is "Africanized Honey Bee". They have made there way into Arkansas and will most likely continue to spread. This Hybrid is generally more aggressive than most European bees. While I have not personally encountered them yet, I have kept track of the situation. A few years ago an American beekeeper/entomologist made a trip to South America to study these bees. Bear in mind that the South American version has more "African" in it than our bees. His report on returning to the states was that while he would not want these bees in his backyard, they were not the menace that our media has made them out to be.
The main difference seems to be that the Africanized bee is much more defensive around the nest. Probably the worst case scenario would be someone allergic to bees accidentally venturing too close to a hive. In any case, and this does not matter weather you are dealing with a European Honey bee or an Africanized version, if for whatever reason you are attacked by bees, LEAVE THE AREA. The old story about if you stand still they will leave you alone is just that, an old story. When the first bee stings you there is a pheromone released by the bee. Any other bees that sense this pheromone will go on the defensive. This means they are looking for something to sting and if you are just standing around, guess who is going to be stung! As to how far to run? Don't know. Helped a pard move a bunch of hives a few years ago and in transporting them they were treated a bit rough. When we went to unload hives they let us know they were not very happy. I made a beeline ( pun intended) for my pickup, while said partner decided he would out run the bees. Did not work. Was not funny at the time, but every at every opportunity said partner will tell about the day I locked him out of my truck. The reason for telling this story is to demonstrate that any honey bee can be aggressive. I have also had hives before that I could not approach within 50 feet without a bee or two or three letting me know that my presence was not welcome. Hopefully most beekeepers will monitor their hives for bees that are overly aggressive and re-queen when this happens. This will keep down the number of Africanized bees in the wild. Also one thing that will help in this matter is that any wild bees will eventually succumb to mites and die out.
If you are out in the woods or around old graveyards,etc. and out of the blue you are stung by a honey bee or as usually the case, you are "buzzed" by a bee or bees, leave the area immediately. Once you are out of harms way then you can start looking for the hive and thus avoid it in the future.