The first thing to keep in mind is that you are measuring a floating signal source. In terms of signal connections, this means that you should either use RSE mode, or use bias resistors in differential mode. Since your signal source has no ground reference, the bias resistors are necessary in differential mode to provide a return path to ground. This is described in Field Wiring and Noise Considerations for Analog Signals.
As you alluded to, the USB-6008 may not be the best hardware to measure this millivolt signal. If you look in the USB-6008/6009 User Guide and Specifications, on page 19 under the Analog Input Specifications, it lists the absolute accuracy as 1.53 mV when using the +/-1V range of differential mode. When you switch to RSE mode, there is only one range (+/-10V), so the accuracy decreases to 14.7 mV.
If you want more accurate USB hardware, you should consider either the DAQPad-6015 or the USB-9215A.
Hope this information helps.