How does one determine the millivolt reading across a Wheatstone bridge?
As drawn you don't know the proper order of subtraction. You would just determine the voltage "difference" across the mV symbol. You could then enter that value at the mV symbol and place the + and - polarity marks as appropriate.  

If the mV symbol had been initially drawn with polarity you would then know to subtract the labeled - side from the labeled + side.