Cops are required to safeguard the property of anyone under their custody. If he hauls you downtown and leaves your bike to *wander off*, the police would be financially responsible for a replacement... even if he's writing you up for everything in the book.

I was briefly detained by a cop once for cycling on private property (a parking lot!) and I verified with him that you are not required to produce I.D. when you are just randomly out on the street.

They sometimes imply otherwise though, to decrease your odds of giving a false name.