Messing around on the outer reaches of the tree with spinnerbaits, topwaters and soft jerkbaits might be a place to start. I'd hit it from all angles, hoping to pick off an 'outside fish' before moving in for the kill.
Then it's a case of slowly working from the outside in. Often a good tree will hold more than one fish, but if you pull the first one out of the middle of the hidey-hole, you'll never know. It's possible, with the right bait, to lead a fish out of the cover, with gentle pressure, before setting on him. This also helps to avoid spooking other bass buried deeper in the tree.
The right bait? My lure of choice would also be a Power Worm (7"/blue fleck) T-rigged with a 1/16th weight. As Hawk said a worm is very forgiving. A light worm even more so. Remember, once you hang up in this cover, you may as well leave it for another day.
As the worm drops, I'd hold it at various levels, giving the fish time to get a good look. The horizontal (or nearly so) branches of the tree let you fish vertically, by letting your bait hang from them. Clear?
There are dozens of trees like the one pictured (and better) on Charleston Lake. Some have 40 feet of water or more at the crown!
CCB- loves playing in the trees...