Braided shield on a pickup lead will always be a ground. It's never a hot. Since the only other wire from your new bridge pickup is the green, that belongs on the first switch terminal, where the white wire from the old one was. And the braided shield grounds to the back of the pot.
Since you're keeping the old middle pickup, it should be wired just how it was originally: ground to the pot, and hot (looks like that one is green also) to the second terminal on the switch.
For the new neck humbucker, are there two wires plus a braided shield?
It would help to figure out which one is the hot, but that isn't too crucial except in terms of phase.
We know one wire will be the hot; all we need to find out is whether the other wire is for splitting the coils, or if it's for ground.
Do you have a VOM to test the pickup? Check the resistance reading between the two wires, and also between each wire and the braid.
That will tell us if one of the wires is a split connection. Once we know that, it'll be easy.
So here's what needs to happen:
1) Reverse your wiring of the bridge pickup - braid goes to the back of the volume pot, green goes to first terminal of the switch.
2) Restore the middle pickup wiring to the way it was at first - ground to the pot, green to the second terminal of the switch.
Then 3) Find out whether the new neck pickup has split wiring or not. I suspect not, but we should make sure before you hook it up.
Finally, 4) Attach the neck pickup once we know what each wire does.