Sure you can, in principle. When you have measured covariates, you can compare their sampled distribution to that of the population of interest. Find enough of a difference (modulo multiple comparisons, significance, researcher degrees of freedom, etc.) and you've detected bias. Ruling out systematic bias using your observations alone is much more difficult.
Even in this case, where we don't have covariates, there are some patterns in the ordinal data (the concept of ancillary statistics might be helpful in coming up with some of these) that would be extremely unlikely under unbiased sampling.
When you have measured covariates, you can compare their sampled distribution to that of the population of interest.
That means that you need more data. Having a standard against which to train your model means that you need more than just the results of your measurement.
You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.