This article explains a biased sensor bridge.

This is a well known biased sensor bridge circuit that you can see in many sensor or instrumentational amplifier specifications/datasheets.

There is another article about a cheaper sensor bridge that does not allow reversing of biasing polarity:

Non-biased sensor bridge is shown in this link:

Supplies

Parts: 1 kohm/10 kohm or 100 kohm variable resistors/ potentiometers, 330 ohm resistors - 2, 470 uF capacitor.

Tools: Multi-meter.

Optional tools: USB Oscilloscope.

Step 1: Design the Circuit

The two outputs (Vi1 and Vi2) can be connected to inputs of instrumentation amplifier.

Using four variable resistors is the only way you can create a biased sensor bridge to minimise the common mode voltage:

Vcm = (Vi1 + Vi2) / 2

The affect of common mode voltage on output is equal to:

Vcmo = Vcm*Ac

(Where: Ac = Amplifier common mode gain, Vcmo = Common mode voltage output)

The output of the differential amplifier is equal to:

Vo = Vd * Ad + Vcm * Ac

Where:

(Vd = Vi1 - Vi2, Ad = Differential amplifier voltage gain)

The minimum the common mode voltage output:

R1b = R2a

R1a = R2b

PSpice simulations show biased voltages (200 mV and 450 mV).