Not strictly Bayesian Statistics as such, but I can strongly recommend ["A First Course on Machine Learning"][1] by Rogers and Girolami, which is essentially an introduction to Bayesian approaches to machine learning.  Its very well structured and clear and aimed at students without a strong mathematical background.  This means it is a pretty good first introduction to Bayesian ideas.  There is also MATLAB/OCTAVE code which is a nice feature.


  [1]: http://www.amazon.com/Machine-Learning-Chapman-Pattern-Recognition/dp/1439824142