Jams and honeys are things that last forever really, they have so little water and so much sugar in them that bacteria denature through osmosis. Honey has been found in Egyptian tombs for pharaohs to have in the afterlife.
Also a fun bee fact, after infection with a fungal parasite, bees use propolis (a sticky substance made of several resins) to self-medicate and to protect their hives against future infection. They also seek out the resin when their larvae are infected, demonstrating once more that bees are concerned with the health of their entire colony, not just with themselves.
So no fungus for bees and honey