What you say is correct. However Lets go back to your original post.
On the arduino analog pins, the difference in voltages relative to ground on the bridge is 0.17 Volts.
When I measure the voltages with my multimeter I read 0.1 Volts which seems more accurate because when I convert the value to temperature I get a more reasonable value.
Can you post the multimeter voltage of A0 to common and A1 to common (aka ground)?
BTW the board @TomGeorge suggested is really the best way to go.
John