My first question to you is, what type of bridge are you used to in this situation? A situation in which you need to rest only your hand on the table.
To expand on what Scott was saying, if you normally use an open bridge, first, you need to develop a closed "cross-over" bridge. It will seem difficult at first and unnatural, but as you use and develop a feel for it, it seems that there should be no other bridges (unless on a rail, or jacked up over a ball,etc).
To do a cross-over bridge, lay your hand flat on the table, then perch up the knuckles of your hand as to cup it. Next, slide your middle finger towards your thumb while lifting your index finger (it will wrap around the cue like a normal closed bridge, but will end up on top of the middle finger, not touching your thumb like the classic closed bridge). Wrap your index finger around the cue, and put your index finger tip on top of your middle finger. Press your thumb snuggly against the inside of your middle finger to aide in support (it's ok if your thumb and index finger touch, but it's not ideal). Most players like to tuck their ring finger under in this case, because it is vestigial (not being used really) and, it looks more professional anyways
Now, all you have to do, to perform the bridge Earl has in the picture, is to raise you elbow and forearm to extend you bridge hand. With your ring finger curled up, you will have just your pinky and your middle finger for support as shown.
Practice with this bridge without raising your arm first, then try it in this situation. this will give you a whole other arsenal to your game, and you will look like an "A" player doing it.
