Bats are a species that live in extremely close quarters. Say a viral disease is using them as a reservoir, this greatly increases its ability to transmit itself to other bats via aerosol or guano. This allows the virus to go through mutagenic changes in its genome to overcome host defense or increase transmittance. As mutations in the genome are driven by pressure or random chance. Now, the virus has both what it needs which is reproduction due to the large number of bats but also since bats are mammals it puts them a little bit closer in terms of protein expression compared to humans. Both bats and humans have similar protein receptors which viruses exploit to gain access to the cell. So, its easier for a virus to make the jump from a bat to a human. Bats are also ubiquitous among landscapes. This tends to give them proximity to humans. Like your rats in your example of bubonic plague. Therefore, contact between bats and humans is unavoidable.

I hope I was able to answer your question!