There is a fantastic
book, if somewhat dated, called Class Construction in C and C++ by Roger Sessions. It does exactly what you're looking for: assumes you understand C, and walks you through the concepts of C++. It hangs on bravely to C throughout the first half of the book, in fact, explaining that you can get many of the features of C++ like vtables, the "this" object, and information hiding, just by using some habits and protocols. Remember that for the first few years, C++ was a preprocessor that turned your code into C code. (Hence weird artifacts like name mangling.)
In the second half of the book, the author finally throws up his hands and says, "We can't go any farther in C. Time for C++, and here's why
." Then he gives the new features (like inheritance) a pretty good treatment.
The book is quite dated (1992), but I found it a profoundly useful read. It's exactly the book you're looking for, I think. It's available at Amazon.com's used book store for $1.10. You'll pay more for shipping than for the book!
http://www.amazon.com/gp/product/offer- ... dition=all
Note that the book won't make you a master of C++. You'll need to go on and read another work, Deitel wouldn't be a bad choice, or perhaps jump forward in time and dive right into the STL. But the book gave me a more solid grasp of the mechanics of C++ than most college graduates.
I put the knowledge from that book solidly to work as recently as 2003, when I was programming in the Windows Kernel, which is a C-only environment. I recommend this book highly to anyone working in C++, even today.
...and knowing why "typedef struct struct Foo;" isn't a syntax error is just gravy.