Have any bridges had goal-posts installed on the approaches?
Where there are hazards from over-head power lines which tall vehicles could make contact with, it is common to have goal posts either side of the hazard, these provide both physical indication of the height limit, they also ensure that the vehicle will make contact with the goal post, which should alert the driver to stop, before they reach the hazard.
That would be my starting point, some form of physical barrier which is designed to be sacrificial, failing safely on impact when a vehicle impacts it but with sufficient noise and disturbance, to alert the driver to stop the vehicle before it strikes the bridge.