For the shielding to be effective you will need to have continuity between the bridge p/u cavity and the neck p/u & control cavities. You'll also want to shield the back of the pickguard as well. No need to do the control plate as it's steel and already conductive.
NOTE: even if the pickguard came with silver paper shielding on it, I still apply copper tape over it because I find the silver paper inadequate (JMO).
You can achieve continuity between cavities and pickguard by running more shielding tape over the edge of the neck/control cavities* so they make contact with the pickguards shielding tape. I like to use the pickguard screw holes as contact points to assure a good solid connection.
To get connectivity between the bridge p/u cavity and the control cavity (since no pickguard) is by running a length of wire from one to the other through the p/u lead hole and soldering directly to the copper tape.
*The shielding doesn't have to extend beyond the lip of the cavity all the way around, but the more points of contact the better. Personally, I overrun the shielding as much as can unless it may be visible, like your bridge p/u cavity.