Measuring low values of resistance directly is tricky. Using a bridge you need to amplify the output with a differential amplifier before applying it to the analogue inputs.
In essence all a bridge consists of is two potential dividers. One provides a fixed reference point and the other will change as the resistance of the one arm changes. So connecting a bridge directly to an Aduino is not going to happen. It needs amplifying first.
In essence you can use any value in the reference leg and in the other led pick a resistance equal to the mid range of your sensor. Drive it with 5V if that does not cause too much current for your sensor or power supply.
A technique you might like to consider is to use the resistance in a variable frequency oscillator and measure the frequency and change.