No you don't need to bridge anything. If you look at the switch on the left it has the inputs from the 3 pickups, the 4th pin is the "mixed" output from the switch. ie the switch connects the pickups together in the various strat combinations, bridge, bridge and middle, etc.
The other half of the switch connects the output across the tone controls, which one being dependant on which position the switch is in. Cutting the two wires from the switch to the tone pots takes them out of circuit, the wire from the switch to the Volume pot stays.
There is definitely an error on the diagram above: The case of the tone pots should also be connected to ground, notice the one leg of the capacitor is soldered to the pot case. Tone pots are connected between "hot" and ground with a capacitor in series thereby shunting the highs to ground depending on the pot setting. See the pinned item on tone pots and capacitors at the top of this section.
Have a look at Mr Gearhead the Fender tech site for more diagrams. Still the horrible diagrammatic form and not schematic unfotunately.
Does anybody know where schematics can be found?
Keith