This SEP article isn't bad, but a better philosophical introduction to Bayesian epistemology is Jonathan Weisberg's "Varieties of Bayesianism" for the Handbook of the History of Logic:

https://jonathanweisberg.org/pdf/VarietiesvF.pdf

Another point to notice is that "Bayesian epistemology" generally means "Bayesianism as discussed by philosophers". There is also "Bayesian statistics", i.e. as discussed by statisticians. Introductions to either of them show surprisingly little overlap between the two "Bayesianisms".