I have had quite a lot of experience with FB/MB trapping. The simplest way to go about this is as follows:
1: Set up a room connected to the caverns. Have the cavern connection blockable with a raising bridge, and chain up an animal inside as bait. Puppies work pretty well. Connect the bridge to a lever, and use this trap setup to capture a web-spitting FB. They are pretty common (unlike GCS, which I only rarely encounter, but they work just as well).
2: Chain up another animal, and build it into a wall of fortifications.
3: On the interior-side of the animal-wall, build a raising bridge (to block line-of-sight to the animal-wall) and fill the rest of that room with cage traps.
4: Get the FB to wander close enough to the wall to start webbing the trapped animal. Webs should spray all over the cage traps.
5: These cage traps can now capture ANYTHING (your dwarfs, forgotten beasts, dragons, elven diplomats, whatever) (except you can't catch anything that produces webs!) so be clever and try to get your target to wander into the web-traps!
Once you get some beasts caged, it is simple to weaponize them depending on their strengths, or to set them up as target-practice if they are one of the unkillable variety. I had a fortress where a giant-glass-man that spewed vomit-causing dust was used to routinely slay sieges. Don't expect your trap setup to work perfectly the first time, though. It took quite a few iterations of the system before a reliable setup was created. Make sure you have appropriate measures in place to take care of things should you fail.