We study learning in Bayesian games (or games with differential information) with an arbitrary number of bounded rational players, i.e., players who choose approximate best response strategies [approximate Bayesian Nash Equilibrium (BNE) strategies] and who also are allowed to be completely irrational in some states of the world. We show that bounded rational players by repetition can reach a limit full information BNE outcome. We also prove the converse, i.e., given a limit full information BNE outcome, we can construct a sequence of bounded rational plays that converges to the limit full information BNE outcome.