We discuss to what extent the current sample of Swift bursts with OA spectroscopy is a biased subsample of all Swift detected GRBs. For that purpose we define an X-ray selected statistical sample of Swift bursts with optimal conditions for ground-based follow up from the period March 2005 to September 2008; 146 bursts fulfill our sample criteria. We derive the redshift distribution for the statistical sample and conclude that less than 18% of Swift bursts can be at z > 7. Finally, by splitting the sample into three subsamples we conclude that the sample of GRBs with OA spectroscopy is not representative for all Swift bursts, most likely due to a bias against the most dusty sight-lines. This should be taken into account when determining, e.g., the redshift or metallicity distribution of GRBs and when using GRBs as a probe of star formation.