There are many reasons, some of which have already been mentioned:

1. Thermoregulatory control - from torpor/hibernation ability and flight gives them a huge range in body temperature, which naturally controls the proliferation of viruses within their systems.
2. Evolutionary development - they are quite an old order in the mammalian kingdom and hugely diverse, like rodents. This means that pathogens have had a long time to evolve alongside their primary hosts and mutate, giving them a higher chance of jumping the species barrier. Many viruses are actually species specific in bats - so if it transmits from it's primary host species to a naive species, it can cause disease. Most of the Lyssaviruses developed within certain species and will cause rabies like symptoms if transmitted to a genetically diverse enough bat species.
3. Flight - bats can migrate, giving them a very large range to spread their saliva, hair and guano to different areas and potentially exposing humans, other species and colonies on their way.
4. Social colonies - these tend to be in sheltered environments, but they adapt to many locations and so houses, bridges, trees and caves are all fair game. Many outbreaks occur through the aerosolisation of bat guano during mining in caves or kids playing in hollowed out trees (both suspected causes of Ebola outbreaks), rather than contact with bats directly.
5. Diversity of colonies - to protect themselves from inbreeding, many colonies are gender specific and progeny are excluded once they mature to find new colonies elsewhere. They can also divide them up as breeding and maternity colonies - increasing the contact with bats from different places and exposing them to pathogens.
6. Long life span - despite their ability for flight and high metabolic rate, they have a very long life span. They can actually recover from certain viral infections and then be reinfected later along with housing multiple pathogens in their bodies (without apparent ill-effect as primary hosts) which increases the chance of sharing of virulence genes and mutations that give pathogens the potential to jump the species barrier.
7. However, they are not protected from any and all pathogens. White-nose fungus is a prime example of a pathogen that has decimated the North American bat population because it has not evolved alongside the species there. One bat that manages to come out of hibernation and fly can spread the fungus to whole colonies and 90+% can be killed.
8. They do many good things for the environment and human health - including protecting us from insect born diseases and pollinating many different types of plants all over the world. The problem lies with the virulence factors that develop within the pathogens in a huge population, that can ultimately cause significant disease if it manages to jump into another mammal species and has the ability to be transmissible between members of that other species (e.g. humans).

There are also unknown mechanisms, for instance bats do not really get much cancer and maybe there is an overlap in the immune response that protects them from cancer and allows them to become very successful primary hosts for pathogens. This is a large area in research and I am sure has more updated knowledge since I stopped studying the field.

For example: recently identified areas for research - viruses housed in vesicles of stem cells of bats, which suggests there's a lot more going on to immunotolerance of bats than we currently know.

https://www.ucd.ie/newsandopinion/news/2023/february/22/firsteverbatstemcellscouldrevealhowcoronavirusesspreadandevadetheimmunesysteminnewhosts/