I am not sure is if non-payment of a bicycle ticket leads to a license suspension. MTO will suspend a license if a traffic ticket (i.e. speeding) is unpaid. What were you convicted of?
Also is your question about not paying the ticket or not paying it on time? If you are stopped on a bicycle, you don't have to show your driver's license, just identify yourself. If you did show the license then the ticket is connected to that. If you don't pay the fine, you won't be allowed to renew your license/plates until you pay it.
So pay the fine and everything will be, pardon the pun, fine. Also bicycle tickets don't carry demerit points, unless you are ticketed in Toronto. They always screw that up. Make sure that no demerit points were added to your driving record.