Unfortunately, the concept you are working towards is fatally flawed, no amount of shielding will make this idea work.
The "battery negative" and the whole circuit represents a floating node, the circuit cannot detect any signal unless it has a reference ground at a potential different from the input. The problem is that you have no other such reference point- unless you connect a wire from the ground of the circuit to an external ground, which I am assuming violates the whole idea of what you are trying to accomplish, this wire would make it work perfectly.
The bird on a wire feels nothing (detects no signal) as there is no potential difference to cause a current flow. Your sensor is the bird- input and ground all at the same potential- no signal.
The "battery negative" and the whole circuit represents a floating node, the circuit cannot detect any signal unless it has a reference ground at a potential different from the input. The problem is that you have no other such reference point- unless you connect a wire from the ground of the circuit to an external ground, which I am assuming violates the whole idea of what you are trying to accomplish, this wire would make it work perfectly.
The bird on a wire feels nothing (detects no signal) as there is no potential difference to cause a current flow. Your sensor is the bird- input and ground all at the same potential- no signal.