Climbing doesn't really develop significant muscle mass, rather, it primarily develops functional strength and overall fitness. You won't notice too much muscle mass gain, or getting bigger. But you will notice a lot of strength gains, especially in your upper body, and especially with your grip.
Of course everyone is different and many people, including myself, do tend to get slightly bigger when getting into shape and exercising more. While I don't get "big", I do tend to gain some noticeable mass, but again, nothing compared to actually lifting weights.
Rock climbing doesn't really get you big and bulky. It can make you stronger though, just without the massive body size.
There are some people who tend to grow and bulk up faster than others, at least to a certain size. They may get some more muscle mass than others, but for the most part, you muscle mass won't really increase that much.
