Is there a GLM bible? Is there consensus in the field of statistics that one book is the absolute best source and completely covering every aspect of GLM - detailing everything from estimation to inference?
 A: It's hard to beat
Generalized Linear Models.
P. McCullagh, J. Nelder.
CRC Press.
2nd edition, 1989
It is comprehensive.
A: I don't think there is a single book that will be exactly what you want.  From your description, I think the best fit would be:


*

*Dobson, AJ & Barnett, A.  (2008).  An Introduction to Generalized Linear Models.  Chapman and Hall.  


It is a classic.  It does cover the math, but is also more introductory than other books that do so.  
A: The closest thing I've found to a GLM Bible is Applied Linear Statistical Models by Kutner, Nachtsheim, Neter, and Li.  It's over 1400 pages and covers linear regression and GLMs.  Virtually anything involving GLMs can be found in that book.
A: 
Is there consensus in the field of statistics that one book is the
  absolute best source and completely covering every aspect of GLM -
  detailing everything from estimation to inference?

No, there is not. However the classic reference about GLM's would be:
McCullagh, P., & Nelder, J.A. (1989). Generalized linear models. CRC press.
A: Introductory books:


*

*An introduction to generalized linear models, by George Dunteman and Moon-Ho Ho (2006). Only 72 pages.

*Generalized linear models : a unified approach, by Jeff Gill (2001) This is also short (101 pages).
Then you have more textbook-like, longer books like the one you mention (444 pages), or the one in the other answer (511 pages).
A: The Nelder book already mentioned is a good one.  
Just for more consideration I would recommend Elements of Statistical Learning Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman.  I Like ESL because it covers such a breadth of statistical and machine learning topics.  It shows how GLMs fit in with other techniques (and it's free).
And as seen in this question, I'd recommend the Simon Wood text  Generalised Additive Models: an introduction with R.  I really believe the Wood text is worth considering because, while it says it covers GAMs, it really covers LMs, GLMs, and GAMs in detail and introduces some mixed modeling techniques as well.  Wood's approach is to introduce each topic with a theoretical background, but then the text is very practical and has examples already in an R package that can be downloaded to accompany the book.
A: A good book is the one by Fahrmeir et al https://www.amazon.com/Multivariate-Statistical-Modelling-Generalized-Statistics/dp/0387951873/ref=sr_1_1?s=books&ie=UTF8&qid=1506715879&sr=1-1  "Multivariate Statistical Modelling Based on Generalized Linear Models (second edition)", maybe not for a first treatment, but for various extensions of the basic model and coverage of computational algorithms. As the title says, multivariate extensions, semiparametric approaches (splines) and extensions to time series, and more. 
