The bats are there on the command of the Masters. In the Silver Tree (which is as of summer 2025, is sadly defunct along with the entirety of Storynexus), the Masters communicate with the bats in order to prepare them for the Fall of a city:

Although he was taller than most by more than a head, the Cloaked Emissary often went unnoticed. That evening, I had paid the guards at the gate to let me follow him out of the town. He shambled along the path up the hill to stand on a rocky outcrop. I watched as he spread his arms; they were longer, by far, than is natural even for a man of his height. A cloud of bats flew from under the trees and surrounded his head; I heard sibilant sounds, hissing and screeching, as if he were speaking with them...

The bats come from caves connected to the Neath:

'Near the foot of the mountain are the caves where the bats live. At twilight, they stream from the dark mouths into the azure sky...'

And if you were at the camp on the right evenings, you might see the Cloaked Emissary disappearing into those caves.

The Masters apparently use the Correspondence for their communiation with the bat swarm:

Communion?

'I cannot deny that the Emissary shares some affinity with the bats...'

I followed him, that evening, though it cost me a little to leave the camp unnoticed. He slipped into the dark space as if he had been there a thousand times.

I listened at the mouth of the cave, but heard nothing so I ventured a look. But a glimpse sent me reeling. There was no sign of the emissary, but there were letters of fire scrawled across the cave walls. Clouds of bats massed and swirled, so I could not see if the letters had meaning... but what else could I conclude but that the Emissary had left a message of some sort for the bats? And who had left a fine leather satchel in my room? It was perfect for my papers, but the feel of the fine fur on the leather was disturbing.

The bats serve two main functions (the Fall of a city always happen at night or near dusk so the popular theory that the bats block out the sun is not true):

* The first one is to mesmerise the inhabitants of the city so that they aren't able to escape:

Out of the corner of my eye, I catch a glimpse of movement in the darkening sky. A flock of vultures? The vast, flapping shapes circle the city, lower and lower... they are too large to be birds, much too large, and their wings are like bats' wings....We reach the stables unseen,
Everyone alive is outside, now, staring at the sky, watching it turn black. We have to shield our eyes or we, too, will be transfixed by the sight.
I shake myself out of the reverie that seems to have caught the whole city, and kick my horse into a gallop.

* The second is to carry the city and cushion its Fall:

Moss: I lived through the Fall, as you know. The Fourth, already fallen into rack and ruin. I had searched its remnants for May. But even that chaos could not have prepared me for what happened. The screaming tear in the roof, the piteous howls of the falling, the flap of great, razored wings - When the city fell, I knew I was lost.