The output of the amplifier changes depending on my distance
It would seem that you have made a very good electrometer or E-Field detection circuit.  It is likely that you are coupling in the E-field from the fluorescent lights in your lab or from the mains wiring around you.  You can prove this by turning off the lights and/or isolating the circuit.

You can solve this by:


moving the amplifier closer to the bridge to reduce the pickup.
extending the shield that you have to surround the sensitive devices (a faraday cage)


You will have to give more details, drawings and pictures to allow peple to fully understand your situation.