My first exposure to Bessel functions was while I was doing an internship and I was attempting to simulate radar imaging on a spherical target. The gentleman that I was studying under had previously written this code in Matlab, and I was attempting to translate it to C++. I purchased this book with the hope that it would help me obtain a better knowledge base to tackle this problem. It didn't.
Later, I took a graduate math course in special functions (Green's Functions, Fourier Transforms, Legendre Polynomials, and Bessel Functions). Although this course was extremely challenging, I found that the examples given in Bowman's text were perfect for the segment of the course that was devoted to Bessel Functions, and it helped me raise my grade on homeworks.
In the end, the book is strictly about Bessel Functions. There is hardly any background (page 1 begins right away with Bessel Functions of zero order). The book progresses linearly with the most basic Bessel Functions, a few examples, and eventually ends with Bessel Functions of any real order and a few applications.