I started at a crossfit gym this week. I am loving it - but the only way I can afford it is the living social deal I found. Consider looking on there and grupon to see if there are any deals in your area.
I doubt you will bulk up. None of the girls at my crossfit gym are bulky. They are trim and have great muscle definition.
As for crossfit arm exercises, the idea of crossfit is to use all your muscle groups - not to pinpoint a specific one. All the crossfit workouts target multiple muscle groups. You can find a bunch of the workouts on Pinterest, but doing workouts with weights, balls, and other equipment can really push you.
"Your past does not equal, nor does it dictate, your future."