I have considerable experience in moving bees (including African Bees) and eliminating yellow-jacket wasps. First let me talk safety. If you are allergic to bees and wasps, you better carry an eppi. pin with you when you are in the wilderness and know how to use it. No to do so is to unnecessarily risk your own life to a preventable problem. All of us should avoid these insects whenever possible, not just because a sting is painful, multiple stings can be serious and even fatal. If you hear a swarm near by (usually bees), move away immediately but keep external activity to a minimum as it attracts their attention. If they are not already swarming you, move away slowly and cautiously. If they are already swarming you get out of there fast; get on you bike and haul. If you are being stung, don't flail wildly, just run like mad and if you can jump in some water, go completely under and only surface for a quick breath when necessary after exhaling under water. (I doubt you carry a straw with you, but your Camel-Bak tube could be taken apart under water and used for a breathing tube. When stung by a bee, the stinger has barbs which make extraction difficult, so the bee leaves you without taking his stinger with him. He will die because of this. You, however, now have a stinger in your skin that is trying to work its way deeper into you. At the external end of this stinger is a small bag of powerful bee poison. If you grab this stinger and its poison pouch with your fingers to pull it out, your fingers will squeeze the bag and inject lots of poison into you. Instead, scrape each stinger off your skin carefully with a credit card, flat object or knife blade.
Swarming bees are a hive of bees that is on the move to a new location. Periodically they stop to rest, most of them hanging on to each other and a branch. Typically they look the size of a soccer or basket ball but are pear shaped where suspended below the branch. Inside the group may be the queen bee that they are all protecting. There will always be plenty of bees who are zooming around the rest either guarding or looking for a place to join the others. Bees are least dangerous and least aggressive while swarming. If you do not disturb or agitate them, they usually will leave you alone. You need to know, however, that any time you swat or crush a bee, it is likely to exude a powerful scent which tells the hive that they are under attack by an intruder. Crushing a bee is a bad idea any time any where!!! It is like throwing rocks at numerous, unleashed, unfenced guard dogs. You are asking to be attacked by a mob.
Wasps are slightly different. Some make large, elaborate hanging nests. If you are looking for trouble, try to knock the nest down or shake the branch it is on. Doing so is like crushing a bee. Most wasps make small hanging nests in dry places and are not much of a threat unless you get close to the nest or disturb it. A wasp sting is more potent than a bee sting but they do not leave their stinger in you, thus one wasp can give you multiple stings. The most dangerous wasps in this part of Florida are the yellow-jackets. A single sting from a yellow-jacket is not more dangerous than any other wasp sting. The danger is in the size and location of their nests. I have eliminated numerous yellow-jacket nests and they are tricky because they are under ground. One nest I eliminated was at least as big as a 50 gallon barrel! Do you have any idea how many wasps live in there? Watching them through binoculars in the daylight it appeared that there were small tornado funnel clouds at each of their numerous entrances. They hollow out the ground, one grain of sand at a time and replace the earth with their paper/wax cones. People have lost their lives by stepping in such a nest and having it collapse under them. The immediate attack by thousands of wasps, is worse than numerous snake bites. If you see the evidence of a yellow-jacket nest, (numerous wasps coming and going) mark the area and report it to the club. In the past we have always taken care of such problems.