A big thing is that Bats have a really weird metabolism, during their day it can dip down to 50 Fahrenheit and then go up to 104 F at night when they are active. This can mean they end up carrying a lot of diseases but not dying/showing symptoms of them. They also have very strong DNA repair compared to other mammals. Then in addition many bats are very social and sleep in big groups, which means the disease can spread throughout the bat population.
Edit: Finally and relevantly they can come in close contact with people by coming into our homes, or people going into theirs. This can let the disease cross over.
> Bats have a really weird metabolism, during their day it can dip down to 50 Fahrenheit and then go up to 104 F at night when they are active. This can mean they end up carrying a lot of diseases but not dying/showing symptoms of them.
Most organisms, including pathogens, have a relatively narrow temperature range they operate in. Hence why we get fevers in order to fight them off. Bats spend most of the time too cold, then get up to the equivalent of a high grade fever for an extended time. Here's a paper on the subject https://pmc.ncbi.nlm.nih.gov/articles/PMC4012789/
That covers the first sentence. How does it connect to the second one? So far, you've described how you would expect bats to carry very few diseases, because diseases that found themselves inside a bat would be killed by the temperature fluctuations. It does not appear to follow that bats should be hosting a lot of diseases at any given time.
You've made an interesting counterargument that I've never come across before. I'm purely speculating here, but maybe the diseases in question (rabies, nipah) are otherwise so deadly that they'd normally just kill the host, but in bats, they linger on. All that to say, that bats aren't necessarily hosting more diseases relative to other animals, but they harbor diseases at the more lethal end of the virulence to transmission tradeoff spectrum.