Effect of bias resistor value on common-mode rejection in a differential or instrumentation amplifier
Please give values used for V1 and V2. It's not that clear what you have used. You should have used V1 at 0 volts to look at CMR. I would also simplify analysis by getting rid of the 10n capacitor...


  I did what you say. I removed the 10n cap and removed V1 and shorted
  Vin and -Vin and made a single node. And I direct coupled the 50Hz 1V
  commonode to that node. And now increasing the Rb reduces the common
  mode voltage when I plot Vo2-Vo1. You definitely are right but I don't
  know why this happens the other way around when I use the way in the
  question.


I think you are getting a mix of V1 and V2 and that was clouding the issue.


  Thanks a lot for this insight. This makes a lot sense now. I dont know
  why in my circuit it is the other way around but your way definitely
  checks the common mode noise rejection. How about is 10k to 100k recom
  a magic?


You don't want the resistor to be too high or you won't bias the inputs correctly. On the other hand you don't want it to be too low or you'll be getting earth ground fault currents (as previously explained on another question).