It would have to be a pretty doggone rigid bridge to stand up to the forces of gravity pulling the edges in towards the center of the earth, which goes against good bridge design. You want bridges to be flexible, not rigid, so that they can expand and contract with temperature, move when forces of wind and nature act on it, and of course allow loads to be carried on them. Because of this, I think such a bridge would collapse immediately. Interesting concept though, if you could create the scenario in a vacuum, somehow find a material rigid enough to withstand gravity, and eliminate all outside forces other than gravity, and execute the support removal instantaneously to get a clean break everywhere, then yes I suppose it might float in theory. Or, if you could make the bridge tall enough that it actually gets into space and is set in a place of orbit, then you could disconnect it and it would "float", or rather orbit...but why would we ever do that now?