> Let's say you are riding your bicycle in a town. The police
> don't like you for whatever reason and stop you for something.
> They demand to see you wallet. You foolishly, or our of fear,
> show it to them.
I don't know about your town, but in my town a bicycle is a vehicle and is subject to the vehicle code which includes showing identification when stopped by the police.
Maybe you picked a bad example here, but if that's the way you ride -- presuming you would only "foolishly, or by fear" identify yourself when stopped by a cop -- then you should probably stay out of California (at least).
http://www.bicyclelaw.com/road-rights/a.cfm/road-rights-identity-crisis
/jordan