Fungi, insects, and worms are probably the most likely sources of below-ground non-oceanic bioluminescence. Bioluminescence seems to be primarily selected for aiding in the attraction of prey, the ability to use a decoy to avoid predators, and communication. My understanding is that bioluminescence is the product of a chemical reaction so I wouldn't expect glowing webs to last long. Glowing edible fungi probably wouldn't fare better than their edible cousins that don't glow.
Perhaps the proximity of your faeries leaves a magical residue that leaves normal matter with a glow. Stones or webs glow dimly as a patrol traverses a tunnel; stalagmites and stalactites glow brightly in warrens or cities. Maybe it builds up based on population and fades slowly: the Ruins of the Great City of the Lost Ones might still be dimly lit after several hundred years.
Another option would be to have the faeries adapted to low light. The underground is probably going to be pretty dark, even with bioluminescent fungi. Your faeries may have exceptional hearing (echolocation) or have developed more and/or more exceptional rods (darkvision). Faeries with a super-sensitive sense of smell might be able to navigate by nigh undetectable breezes or scents from the surface (or the depths). It'd be hard to describe; but, they may be able to detect slight variances in their planet's magnetic field and navigate based on known veins of ore, as an example.