Lowered bridges can be destroyed. The bridge itself can't be destroyed when raised, but the mechanism can if it's "located" in an exposed tile, i.e. if the mechanism is "located" under the raised bridge or inside of it (when viewed from the attacking heat source) it is protected (and that protection is lost when the bridge is lowered).
If you have a two tiles long bridge the mechanism ends up under the same tile regardless of whether the bridge opens towards the east or west, and the same tile regardless of whether it opens towards the north or south. This means that in half of the orientations the mechanism is vulnerable (and I don't remember with certainty which tile it's placed on).
A raised bridge is invulnerable regardless of what material it is made out of (including things such as ice). The mechanism can be destroyed if exposed and not made out of a resistant material (exists for magma, but I don't think even adamantine is safe against dragon fire), but the bridge will then remain locked in the raised position, and thus still remain invulnerable.
It's possible to attach a new mechanism to a raised bridge (it probably requires access to the tile where the mechanism is to be installed, although I'm not certain. If it does, it may be complicated in some cases, such as when that location is covered by magma). Once a new mechanism has been installed, the first pull of the lever (or whatever activation is used) orders the bridge to be raised, and as it is raised already nothing happens. The second one orders the bridge to be lowered, which returns the bridge to the lowered base state. Attaching a mechanism to a raised bridge causes the same kind of situation as you get when a bridge is activated twice in too quick a succession so the second activation happens during the "cool down period" and so is ignored.