Bee
A bee signals that what you gathered diligently comes back as something sweet. Traditional reading unexpectedly took being stung as a good omen and read it as a windfall or as a conception dream. Seeing a hive or gathering honey is a time when what you built is harvested, and a swarm arriving means people are gathering to you. If you were chased and the fear was strong, by contrast, read it as a relationship or a task that weighs on you.
A bee both gathers industriously and stings, and dreams carry those two strands together. A bee stings only as a last resort, and the sting costs the bee its own life. Being startled is no reason to call it ill-omened. If a hive appears as well, it stands for something built by many hands, and its condition is worth noting.
Readings by Situation
Being stung by a bee
Tradition read this as a good omen of unexpected wealth, and some readings took it as a conception dream. Whether it is one, though, is better judged by circumstances than by the dream. If surprise outweighed pain, it reads well.
Seeing a hive or gathering honey
A good omen that what you built is harvested. Tradition read honey as a valuable result. If you have prepared something for a long time, this is the reaping.
A swarm gathering around you
A sign that people are congregating to you. Tradition read a swarm as your circle widening. If it was more than you could handle, though, it also signals that your share has grown.
Being chased and afraid
A sign of a relationship or a task that weighs on you. What separates this from the favourable reading is the size of the fear. Judge which by how you felt on waking.
A bee dream is not an ill omen. Bees move as a swarm, so the dream comes more often when something is under way with other people than when you are toiling alone. If you were stung, look at who the matter is tangled with rather than taking fright.