The Batcycle is pretty common in canon, but it's always been a motorcycle. I can't find any references to Batman riding a completely unpowered bicycle (even in the campy Golden Age/Adam West era). Has it happened?
I give you Batman #29 (June 1945), with Batman and Robin on penny-farthings:
Note that like the cover of World's Finest Comics #54 (props to RoamingShroob), the depicted scene seems to be a gag cover that doesn't appear in the issue itself.
The title page for the story "City without Guns" (Detective Comics #196, 1953, reprinted in Batman #223, 1970) has an image of Batman and Robin riding penny-farthings on a London dock, but once again the image doesn't appear within the content of the story.
I don't really understand the fascination with penny-farthings, but Batman rides a weird backwards one (with Robin in some kind of sidecar) in "The Famous First Crimes" (World's Finest Comics #25, November 1946); this one appears in several frames of the actual story:
I did find an unattributed image of Batman fighting crooks from a regular bicycle, but I don't remember this, and I haven't been able to track it down yet.
But it does seem that yes, Batman has been depicted riding a bicycle.
(There is also a scene at the start of Batman: Black and White #5 (2021) where Bruce Wayne and Damian are riding mountain bikes to case out the site for a later operation, but I don't include that since it's not Batman riding the bicycle.)