The mounting holes on $1-2 readily-available, 15 Amp lever micro-switches make it easy to gang (align) them together side by side. This effectively makes a single-piece 3-pole micro-switch. Considering the width of a 3-track bridge it seems mounting it would be no more difficult than a single micro-switch.
Not sure how you feed power to the tracks on the bridge - presumably from both blocks on either side of the bridge? If the connections are good enough it also seems you could power the blocks on one side via the bridge tracks from the other side. That way, as soon as the bridge goes up it cuts power to the other side. That way you only need a switch on one side.
Finding a suitable 3-pole relay could get spendy relative to about $5 for 3 micro-switches that would switch track power. Would also require more wiring since you need to bring in external power for the relays as you're running conventional track voltage. If you only want a micro-switch on one side of the bridge, same issue as above. If you don't run track voltage through the lifted bridge track, you'd need another 3-pole relay on the other side plus a wire "tether" of some sort to get the micro-switch relay control signal across the raised bridge.