Snap off an arm's length of thread and attach wax to both ends. You can find invisible thread at magic supply stores.
Attach one end of the thread to yourself by sticking the wax snugly behind your ear. The other end will be attached to a random nearby object to create a stable support line for the dollar bill to hang off of.
When you perform the trick on the fly in front of an audience, subtly stick the waxed end of the thread that is not already attached to your ear onto the anchor (anything with enough weight to support the thread and a bill; furniture or a book would work fine). This will create an invisible line between you and the anchor. Ideally, the anchor will be close to you and at about chest level so you don't have to worry about spectators hitting the thread.
Borrow a dollar bill from a spectator. Crumple the bill quickly in your hands and tell the audience that through the power of static electricity you will make the bill levitate. Meanwhile, form the crumpled bill around the thread so it rests on its own, but leave your hand underneath as if you are supporting it in your palm. Remember, there is no wax holding the bill to the thread, so handle the bill with care so it doesn't fall off.
Slowly tilt your head back a little and the bill will rise into the air. This is why the anchor should be about chest level. If it were on the ground, the angle of the thread would be such that the bill might slide to the floor. Once you've raised the bill, lower your hand and let the bill appear to float in midair. Wave your hands above and below the bill to trick the audience into thinking there are no strings holding it up. As you're doing this, you can move your head back and forth slightly to make the bill rise up and down seemingly on its own. Your dramatic hand movements should mask your minor head tilts.