Do you want to be able to make quick, specific adjustments? Then a small value trimmer in series or a very large value trimmer in parallel would do it.
Do you want to simulate a more analog effect? How about a power FET in contact with one of the resistors acting as a heater? The temperature change will change the value of the resistor based on its tempco. The heat will transfer to the entire bridge over time, but the resistor in contact with the heater will experience the most sudden change, upsetting the bridge. Flip the heater on and off to simulate disturbances.