It’s not that such a bridge cannot be rebuilt, but rather that in this version of Asgard, at least, it cannot be “magically” rebuilt with a wave of Odin’s hand.
Given how the “bridge cannon” itself seems to work, there seems to be some form of scientific basis around wormhole and/or teleportation theory (and throughout the movie, as much is said). The technology to establish such wormholes seems to have existed in but one location on Asgard – whether that is a security measure to ensure a single route for any large scale invasion, or due simply to the massive energy resources required or other unseen operational costs remains unknown.
The ending makes it pretty clear: Thor will next be seen in The Avengers, and in order for that to happen, he (or perhaps his new flame Jane Foster) will need to find a way to bridge the worlds once more. My guess is that restoring the Bifrost bridge will take approximately 1 year of godly effort – or just in time for Thor to appear onscreen next to the Hulk, Captain America, and Iron Man(*).
(* Just as likely, this plot point will be completely ignored, giving fans yet another thing to discuss once the ensemble movie is released. 😉 )