Do you live in the United States? In the U.S., despite what officers tell you, you do not have to identify yourself when asked. The only exceptions are if you're in a vehicle or in an airplane. And in some states they can demand if you they believe you are connected to a crime (California is not such a state)
I am assuming SF considers a bike a vehicle so fair game I guess. But you cannot just beat up or arrest someone just because they refuse to show their ID. You cannot assume suspicion because they won't tell you who they are. You're essentially saying if you got nothing to hide, you shouldn't worry about telling police who you are.
One time I found a wallet on a sidewalk, I picked it up, saw there was ID. The police station was nearby so I drove to turn it in. When a cop showed up (the station was closed for the night), I explained to him that I found a wallet and was turning it in. He asked me a couple questions and asked me if I wanted to leave contact information, I hesitated, and eventually after the officer assured me he didn't care, I said, "no." But during that moment I seriously considered whether or not I had to assert my right to remain anonymous/not show ID, especially since I was just trying to be a good Samaritan, and didn't want to deal with any possible accusation of stealing money from the wallet (it was empty).