Even without an allergy, enough bee stings can kill a grown man. Though the threat of death is usually minimal in a bee swarm situation, it's still worth avoiding, namely because being stung is bad for both you and the bees. In fact, bees aren't natural aggressors, but they aren't very smart either, so should you find yourself in a situation where you've been mistaken as a threat to the colony, or you were stupid enough to throw rocks at a hive, then here's your best exit strategy.
Sprint away from the swarm as quickly as possible. Bees can fly at a top speed of 15 miles per hour though they usually fly around 9 miles per hour. Depending on how angry they are and the type of bee, you might be able to out run them but not for very long. Some types of bees are more determined to hurt you for downing their hive and will give chase for over a mile.
Get indoors if possible. If you are in a residential area or near a car, put windows and walls between you and the bees. It's likely that a few will follow you in, but 1 or 2 bees are easier to contend with than 700.
Head for thick brush if you are in the wilderness. Tall grass, bushes, high weeds, or dense forest will all help you out considerably. Though it may slow your progress some, the vegetation actually provides cover for you. If chasing you becomes complicated, bees will often lose interest.
Divide and conquer. If you are with someone else, split off in different directions. With more than one aggressor, bees will become confused and disband. You will likely both have bees chasing you, but contending with half of a swarm is better than a whole.
Maintain a straight trajectory. Don't zigzag through a wooded area because you will be crossing ground you've already been over and can potentially pick up stragglers. Always keep a straight line directly away from the hive.
Remove the stinger as soon as possible if you are stung because it will continue to inject venom as long as it's embedded. To remove a stinger, drag your fingertips over it as though you were scratching a deep itch. Squeezing a stinger to remove it can cause the remaining venom to release into you.