Is it important to 'trap' it between the bridge and body? Or does it just need to touch the bridge?
It only really needs to touch, but it also needs to stay put. For example if it's so loose that you can break the connection by shaking the guitar around, you'll get an intermittent crackling sound.
On most guitars the ground wire is held really solidly. With tune-o-matics the wire normally goes from the control cavity to one of the holes the mounting stud bushing is pressed into, so it touches the bushing, which touches the stud, whch touches the tailpiece, which touches the strings... you get the picture. :)
On Teles and hardtail Strats, where the bridge is screwed flat on the body, there's normally a hole drilled from the area under the bridge to the control cavity. Then the bare end of the wire is trapped between the metal bridge and the body.