It depends where you are
Strike for Cause
In jurisdictions where you can strike for cause the judge would hold a trial to determine if this was a sufficient cause to exclude the juror. The specifics differ by jurisdiction but taking new-south-wales as a generalization:
[t]hat the proposed juror does not possess the necessary qualifications or that he has some personal defects which render him incapable of discharging his duty as a juror or that he is not impartial or that he has served on another jury in respect of the same matter or that he has been convicted for an infamous crime.
In many jurisdictions (not england) each side may have the right to a limited number of challanges without cause. For example, in new-south-wales, that number in criminal trials is 3 (plus 1 if more than 12 jurors will be empaneled - this is often done to provide"spares" in long trials).
To exclude all cyclists you would have to convince the judge that all cyclists are biased - not an easy task