It has been hard for me to guage just how fast it grows. But I started with a sandwich baggie-sized portion back in January, and now I have masses of it in 5 tanks, plus one mini grow-out tank, and my half-barrel pond. It seems to grow most slowly when just left floaiting in a clump, reportedly due to only the outside portions getting the most light. When I thin it out, I start seeing little verdant-green growth spreading out, attaching to driftwood. Don't be afraid to attach little bits to stuff, as it will eventually start filling in, given enough light (CO2 certainly helps too).
One annoyance with Java Moss, especially in a clump, is that it is like a magnet for debris. Happily, my new Cherry Shrimp have been great for cleaning it up.