Admitting 'it was you' isn't enough without evidence...

As Tabetha said, it's up to them to prove beyond a reasonable doubt that YOU were riding YOUR bike, and that upon your request you should be able to obtain a copy of any evidence that could prove/disprove your innocence.

You can also ask for a copy of the most recent calibration records for the camera that took the picture - they're supposed to be calibrated quite regularly, and if that camera's not been recorded to have been calibrated recently enough, its pictures can't be used as evidence because they could be innaccurate.