As the producer and writer Jordan Peele says, what Candyman wants more than anything is to be eternal, and he achieves this through killing his victims and being ingrained in the psyche of those who believe in him. After Burke's encounter with Candyman, the film fast forwards 42 years to 2024.
In sum, that Anthony's spiral into Candyman could be caused by an insect attack is actually not as far removed from reality as you might think it's just definitely a wasp, not a bee.