@Richard's answer clearly establishes that bats were at one time present in the Batcave. If there has been substantial construction work since then, the bats would need to have been relocated; they could not possibly have survived in situ with major renovations going on.
But building a bat house is quite easy and inexpensive (even quite a large bat house should be affordable for BW) and would be a logical precursor to the renovations.
So evidently the reason the bats are no longer visible in the movies is that they've been relocated to a bat-house in a safer and quieter part of the Batcave with less vehicles, visitors, bright lights, etc.
If they do live in a bat-house then it must surely be known as the Bat-bat-house.
Or on a less optimistic note, perhaps they've succumbed to white-nose syndrome, which seems to be endemic in Gotham City:
We have yet to find a cure for the disease known as white-nose syndrome, which has decimated populations of hibernating, cave-dwelling bats in the Northeast. ...
White-nose syndrome (also known as W.N.S.) was first documented in February 2006 in upstate New York, where it may have been carried from Europe to a bat cave on an explorer’s hiking boot. In Europe, bats appear to be immune, likely the outcome of a long evolutionary process. But in North America, bats are highly susceptible to the cold-loving fungus that appears in winter on the muzzle and other body parts during hibernation, irritating them awake at a time when there is no food. They end up burning precious stores of energy and starve to death.
The consequences have been catastrophic. A 2011 study of 42 sites across five Eastern states found that after 2006 the populations of tri-colored and Indiana bats declined by more than 70 percent, and little brown bats by more than 90 percent. The population of the northern long-eared bat, once common, has declined by an estimated 99 percent and prompted a proposal from the United States Fish and Wildlife Service to list it as an endangered species. Other species of hibernating cave-dwelling bats have declined precipitously as well.
Whether these bats will recover or go extinct is unclear.
Protect Our Bats, New York Times, 11 May 2014
Whitenosesyndrome.org, U.S. Fish and Wildlife Service