The problem with that idea is that bridge rectifiers raise an alternating current to its peak voltage. Wall current is 120 volts RMS, but more like 170 volts peak to peak. V[sub]peak[/sub] is what the filter capacitor will be charged to in an unloaded condition, such as when the light switch is off. Turn the switch on, and you'll have one hell of an inrush current across the cold filament, which will be even stronger than the inrush current from a 120V[sub]RMS[/sub] source (and remember that tungsten filaments have a negative temperature/resistance coefficient that causes them to burn out most often upon being turned on). Under load it will drop to something closer to 120V, but that all depends on how loaded the rectifier is and what sort of load is connected to it (inductive, resistive, etc.) and the higher voltage upon turn-on will kill the lamp quickly.
Honestly, a run-of-the-mill COTS (commercial off the shelf) surge suppressor is your best bet.