It not clear to me what kind of book your looking for, or at what level.  Or perhaps it would be better to say I don't believe that you have a dichotomous classification into books that only teach mathematical content versus how to do mathematics.

At a very elementary level, one book which hasn't been mentioned yet is

 - _How to think like a mathematician_, by Kevin Houston

that I've sometimes used as a supplementary book in an intro to proofs course.

Then after one progresses to a more advanced level, I think one learns the art of mathematics not so much by explicit meta-construction, but by seeing it and figuring it out oneself.  That said, there are some books which help with this more than others, and here are a few more specialized ones that I think are good:

 - _Course in arithmetic_ (or anything) by JP Serre (he's very concise and on the surface you might place this in your first category, the presentation and choice of material is excellent, and I think the _process_ of reading Serre and figuring out the details helps one's mathematical maturity greatly)

 - _Problems in Algebraic Number Theory_ by Murty and Esmonde, or similar books in this vein (there are some basic definitions, and then a load of exercises (with hints and solutions at the end) for you to develop the theory on your own, a quasi-Moore method sort of thing)

 - _Foundations of Algebraic Geometry_ notes by Ravi Vakil (he has lots of meta-mathematical notes on why you do things a certain way, that I think help mature one's mathematical philosophy)