I would make the bridge work at a much higher impedenance level and use a instrumentation op-amp. So two top bridge resistor make 10,000 ohms, and these need to be closely matched, maybe make the one in the reference leg 9.1K ohms in series with a 1k trim pot for balancing the bridge. The lower reference leg can either be a 19 ohm precision resistor or a 100 ohm trimmer pot to better match the 'zero' starting value of your sensing resistor. You can easily do the math to see what the top and bottom millivolt output of the bridge will be for your sensor and then decide how much gain you will have to set up in your op-amp.
Lefty