I walked past a guy standing outside the Palo Alto Creamery, and he was reading from a copy of Misner, Thorne, and Wheeler -- it's a very distinctive looking book. Turns out he was a guy with a non-math background who had taught himself enough to follow the book. I was impressed!

That book is big enough to visibly distort space-time on its own.

I'm impressed that the reader learned the math on his own. And, uh, what's my excuse?

I would also recommend "The Large Scale Structure of Space-Time" by Hawking and Ellis. It uses some advanced mathematics and some prior knowledge of GR, at least at the level of Schutz or Carroll, is needed, but it is a wonderful book to learn about the global structure of spacetimes with black holes, singularity theorems and so on.

Carroll is a graduate-level book, and MTW is notorious. I'd start with Hartle, or something even lower-level.

My undergraduate course used Schutz and Carroll. I think, as long as you are comfortable with both proof based and dirty mathematics, you can start with physics grad texts. In fact, a lot of times, the concepts are easier to understand with more conceptually elegant mathematics.