iVillage

This probably comes from the ancient practice of burying bones in the foundation of a new bridge for good luck and also to make magic that will keep the bridge from falling.

Make a wish while crossing a bridge; it will be granted if you do not speak aloud until you are across. If you go over a bridge you've never crossed before, lift your feet off the floor of the vehicle you're riding in and make a wish. (The driver, for obvious reasons, is not supposed to make a wish.)
(Maryland)

If you cross a bridge in an automobile, hold your breath until you reach the other side and make two wishes: one as you get on the bridge and one before you get off. (A very long bridge might present a problem.)
(New Jersey)

When you cross a bridge you've never crossed before, make a wish in the middle of it.

If you walk over a bridge you've never walked over before, jump three times after every twelfth step, and you can make a wish just before stepping off the bridge at the other end.

Breaking stride to jump while on a bridge may have its origin in the military practice of having troops "break cadence" while crossing bridges; the steady marching rhythms hammer the bridge's supports, which can be destructive.

If you walk over a bridge you've never walked over before, stop halfway across, look first upriver (or up the valley or ditch), then look downriver (or down the valley or ditch), jump three times, make a wish, jump three times again, look downriver, and then look upriver.

Spit three times from a bridge into the water as you make a wish.

Count to thirty-three by threes as you go over a bridge and then make a wish, repeating it three times.

If you go under a bridge, make a wish. (Another custom is to cross your fingers as you go under a bridge so that it won't fall down on you.)