Will confirm what Dave H. just said about structural capacity. If the bridge is strong enough trains will have no reason to slow down. Running at a slower speed reduces the dynamic load on the bridge. The railroads hate having a speed restriction on a bridge, but also they hate spending the millions that may be required to replace a large bridge. For a busy main line it will be high on the wish list, fighting for capital funds. On a secondary line the engineers will do as much as possible to extend the life of a weak bridge, which often means a permanent speed restriction to ensure the operation is safe.
Temporary speed restrictions may be imposed if a defect is noted in one of the structural elements, until it is rectified or stabilized. They almost always are imposed when the bridge is being repaired or upgraded, especially when there are temporary supports or jump spans.
Sometimes too, the speed restriction will apply only if the train includes cars over a certain weight, or type. Ore cars in particular are short and heavy.
I think movable spans are likely to have a speed restriction but in this case it may relate more to easing the stress on the special castings at the joints.