On the surface, this seems like a very, very stupid question. After all, rust will occur when an alloy or iron is exposed to moisture and oxygen for an extended period of time. When this happens, the metal will begin to corrode and the bonds will be weakened. In other words, wood is not going to rust so why on earth is this even a question. It is simple; you may need to worry about rust in a wooden bench if the frame is made of metal. Not all wooden benches will feature metal components, but some will.
From there, it boils down to what the frame is made out of. If it is made out of casting aluminum, you are safe as this has no iron in it. But, other metals such as steel or wrought iron can potentially rust if they are not protected from it.