Amplification of Bolometer
You can directly measure the voltage with a 24-bit ADC. If you have ENOB of (say) 20 bits and a full scale range of 600mV your resolution is about 600nV, so you can measure the 129uV to a resolution of about 0.5%.
Chances are your reference divider won't be stable to 1ppm for very long and there are other issues with keeping noise and thermal EMFs in check, but that's the 50,000 ft view. The ADC reference should be ratiometric to the bolometer excitation (ie. dervived from the same reference voltage) so it cancels out, because a 1ppm reference is both very difficult to achieve and unnecessary.
You could also build a full Wheatstone bridge with ultra-high precision resistors to buck the voltage from the pair of resistors in the bolometer, then the ADC can measure the difference in voltages, which can be amplified first.
In the case of the Langley bolometer both halves of the Wheatstone bridge were part of the construction of the sensor, which is obviously preferable so that various inaccuracies and drifts cancel out.