That book isn't bad. As a math major, you may like this more
http://www.amazon.com/Introduction-Game-Theory-Martin-Osborne/dp/0195128958
I like Binmore, but it's not the most straightforward, though it has more mathematical proofs than others. The most concise is Gibbons. It's graduate level but nothing in it would be hard for a math major.
It's not going to be very satisfying for you. Bayesian games just mean players have different information at various point of time. So posterior beliefs are formulated using bayes rule.
Auman wrote a paper about the rational beliefs and common priors in this famous paper
http://www.dklevine.com/archive/refs4512.pdf
For learning about Bayesian Nash Equilibrium, pretty much any Game Theory text will have it (upper level undergrad). Obsborne is probably the most popular one http://www.amazon.com/Introduction-Game-Theory-Martin-Osborne/dp/0195128958
I personally like Harrington who I find does a good job with Bayesian NE.
But any book covering Harsanyi and Selton (games of incomplete information)