If we have an ingress/egress easement that crosses a seasonal creek, do we have the right to build a bridge across the creek to be able to access our property when it rains?
No, you do not have the right to build a bridge on his land. The easement is nothing more than the right to travel over the land as it is; it does not give you any other property rights or any control over the neighbor's property. This means that you can't erect any structures or make any changes to the land, such as by building a bridge. All you can do is travel over the land as it exists. (If there had been a bridge, he could not tear it down--he cannot do anything to impair the use of the easement. But he doesn't have to do anything to make it more usable than it is, either, and does not have to let you do anything to improve it.)