It would need to be designed to withstand the "head pressure" of the water at the deepest it could ever be expected to reach. Unless the river was absurdly small, the change in depth caused by a ship displacing some of the water would by too small to measure. It would be more important to take into account seasonal variations and historical high water points, and even ship's wakes. A safety factor would be applied to cover all the minor unknowns.

But just for fun, keep in mind the ship has its effect whether its under the bridge or a mile upstream. So really the ship was probably already in the water when the depth was measuredm, and so was part of the calculation even though it wasn't considered. Ships come and ships go, but they're always there, and their average dispacement affects the depth...but not much!