Quite simple really. How large can a bat grow before it is too big to fly. I would like a bat with a similar external and internal structure to a real bat just scaled up. I am willing to accept changes to the wing to body size ratio as I assume that bats can't get that much bigger than they currently are by simple scaling up due to the square cube law.
The worlds largest bat, the Golden-Crowned Flying Fox, weighs in at a wingspan of 1.5-1.7 meters and a weight of only 1.5-2.6 lbs. But with these estimates, we can absolutely do better.
Introduce Argentavis, the largest bird ever to exist weighing in at an impressive 154-159 lbs with an estimated wingspan of 23 feet! Doing fancy math and applying the square cube law we get a bat size of 8.85-14.21 lbs for a bat with an equal height to Argentavis. But you know what they say, go big or go home.
Behold the king of evolutions air,Quetzalcoatlus, weighing up to an estimated 550 lbs with a theoretical wingspan of 10 meters (32 feet 10 inches), this was the largest animal to ever fly. Again scaling up the Golden-crowned Flying Fox using the square cube law we get a bat of equal size should weigh in at around 39.6 pounds, now while this seems odd, keep in mind 2 things.
- Mega bats, such as the Flying Fox, tend to fly much the same as Quetzalcoatlus is theorized to, mostly gliding with short burst of energy to increase height.
- Mega bats are known to weight a lot less than they appear, as I said before, the Golden-Crowned Flying Fox only weighs at most less than 3 pounds!
Now how you're going to keep a bat this size alive is another manner as it will need to almost always be eating food very high in calories and fat, but I'll let you save that for another question.
I'm assuming by your question, you're trying to re-create something like the man-bat from the Batman series. If I'm wrong here, please correct me.
I've been researching and found that the largest current bats that exist are the Giant golden-crowned flying fox species native to the Philippines.
Bearing in mind that this bat has a wingspan longer than most humans are tall and that if this image is to be believed, then it's fair to say it's pretty big anyway.
Now, onto your question, could they get any bigger? In all honesty probably not any time soon.
Not only do we have the square cube law to take into account as you previously mentioned in your question, but you've also got the dynamics of the Planet to take into account.
During the age of the dinosaur, scientists think that the composition of the atmosphere had much more Oxygen than we do right now and that that contributed almost proportionally with the size of the dinosaurs.
Since the Industrial Revolution, we humans have been introducing carbon emissions and greenhouse gases into our atmosphere, we're slowly killing off the trees that produce oxygen and the corals in the seas (which are made of carbonaceous material) adding more carbon dioxide into the system.
TL:DR - Probably not until we either stop polluting or die off.
TrEs-2b gave a very good answer. I'll just add in a bit of bat physiology which might explain why modern bats don't get as big as giant pterosaurs.
Bats are warm-blooded. Their wings are made of living membrane through which blood flows. This means that bat wings are great for shedding heat when the bat gets too hot: a huge surface area to do just that. But conversely they are rubbish at retaining heat when the bat gets too cold.
All the really big bats live in the tropics. Something the size of a fruit bat would chill itself to death in the likes of Canada or Norway as heat leaked away from its wings every time it flew. Even the microbats (microchiroptera) have to take measures to avoid the cold: hibernating or migrating away.
So make it a fruit bat (megachiropteran or megabat) type of bat, and have the climate of the place it lives exactly right for getting huge yet staying not too hot and not too cold. Of course, the megabats don't have sonar - you don't need echolocation to catch fruit. So if you want a bat with sonar, those are out.
Now obviously the pterosaurs also had naked membrane wings and DID get enormous. So they cracked the staying warm problem.
Even though I can't give an estimation of factible size for a bat. There is a problem with an important function of bats if you make them grow, the function of their radar.
Bats have a radar which works using sound, so if you increase the size of a bat, then the radar lowers its frequency. Therefore, even if the bat can fligt, probably it cannot find food, unless it changes its diet.
The second problem would be the diet, a bigger bat needs to find preys bigger as well, otherwise it will waste too much energy to find more small preys.