A healthy bobcat is a threat to house cats and small dogs, but I wouldn't worry about it causing problems with children or larger dogs.

If you want to trap it, I would use a large cage trap. The trap needs to be tall enough the cat can enter it comfortably. Place the trap where the bobcat wants to natrually enter the trap, like between some brush, where the cat is naturally funnelled to the trap entrance.

For bait, you can use a variety of things. I trap coons, but have caught bobcats, using dry cat food. Canned cat food or a can of tuna also works. But if you have coons, you may catch 20 coons before you catch one bobcat.