Why don't rats have a gallbladder, unlike other rodents?
There are many different theories on this aspect of evolution, some of them are proved and others are just conjectures. Materials and research in this particular aspect is very few. Here I tried to provide an answer in reference to the particular animal you mentioned, i.e. rat.

Rats don't have a gallbladder possibly due to the following reasons - 


The concentrating power of bile in rat's liver is high, so the main function of bile concentration by gallbladder is unnecessay in them. This is probably the most supported theory regarding this.
Rats frequently take their food so they require a continuous supply of bile. This eliminates the necessity of bile storage.
Harbivore animals relatively lack fat in their food. This reduces the need of large amount of bile salts in the intestine. 


References - 


https://theparadigmshiftgroup.com/animals-no-gallbladder/
Zoology textbooks
http://www.sciencedirect.com/science/article/pii/S0375090613000323?np=y