I had a birch stave that I removed the bark, and split it, and it dried down to 12% in less than two months. Granted that was in January, and during that time of the year the air here is very dry, and I had it in a room with a wood stove and a fan. So that is probably ideal conditions for rapid drying.
Birch leaves a lot to be desired as a bow wood, but I've just about finished a 50 pound knotty birch bow, and I have to say I'm really liking it. For dimensions, its 65" long tip to tip, and about 1 3/4 wide at its widest right out of the fades. Only final finishing left, can't wait!!
It's definitely a second tier bow wood but I've got proof out in the shop that it can work. I'll probably have pictures up here soon