Practice is the best way to learn. I've used one hand in favor of the bridge for most shots since I saw someone do it many years ago. I don't recommend shooting without a bridge of some sort (rail or an artificial bridge) for long shots (big distance between cue and object balls) until you've practiced it a lot. A guy that I played in APA a few years ago used a small sand bag when he broke his arm. He played really well with it. In fact, I think he played better with the sand bag than he did after his arm healed (just judging from the short performances during league play). Either way, you're going to need lots of practice.
When I shoot one handed, I usually don't have any bridge (jacked up, I think they call it). I hold the cue as steady as I can (which isn't really very steady), then stroke it when the tip is close to where it needs to be with kind of a jab stroke. It's pretty darn effective and actually works better than the bridge would on some shots. I used it during a runout last night in league. I'm definitely better shooting that way than I am using the rail for a bridge, but that's mostly due to me practicing the one and not practicing the other nearly as much. Don't worry, it'll take a while, but you'll get it.